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A176226
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A symmetrical triangle sequence: T(n, k) = q^k + q^(n-k) - q^n, with q=5.
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4
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1, 1, 1, 1, -15, 1, 1, -95, -95, 1, 1, -495, -575, -495, 1, 1, -2495, -2975, -2975, -2495, 1, 1, -12495, -14975, -15375, -14975, -12495, 1, 1, -62495, -74975, -77375, -77375, -74975, -62495, 1, 1, -312495, -374975, -387375, -389375, -387375, -374975, -312495, 1
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OFFSET
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0,5
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COMMENTS
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Row sums are: {1, 2, -13, -188, -1563, -10938, -70313, -429688, -2539063, -14648438, -83007813, ...}.
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LINKS
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FORMULA
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T(n,k) = q^k + q^(n-k) - q^n, with q = 5.
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EXAMPLE
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Triangle begins as:
1;
1, 1;
1, -15, 1;
1, -95, -95, 1;
1, -495, -575, -495, 1;
1, -2495, -2975, -2975, -2495, 1;
1, -12495, -14975, -15375, -14975, -12495, 1; 1, -62495, -74975, -77375, -77375, -74975, -62495, 1;
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MAPLE
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q:=5; seq(seq(q^k +q^(n-k) -q^n, k=0..n), n=0..12); # G. C. Greubel, Nov 23 2019
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MATHEMATICA
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T[n_, k_, q_]:= q^k +q^(n-k) -q^n; Table[T[n, k, 5], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Nov 23 2019 *)
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PROG
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(PARI) T(n, k, q) = my(q=5); q^k +q^(n-k) -q^n; \\ G. C. Greubel, Nov 23 2019
(Magma) q:=5; [q^k +q^(n-k) -q^n : k in [0..n], n in [0..12]]; // G. C. Greubel, Nov 23 2019
(Sage) q=5; [[q^k +q^(n-k) -q^n for k in (0..n)] for n in (0..12)] # G. C. Greubel, Nov 23 2019
(GAP) q:=5;; Flat(List([0..12], n-> List([0..n], k-> q^k +q^(n-k) -q^n ))); # G. C. Greubel, Nov 23 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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