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A349682
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a(n) = A000292(6*n + 1) where A000292 are the tetrahedral numbers.
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1
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1, 84, 455, 1330, 2925, 5456, 9139, 14190, 20825, 29260, 39711, 52394, 67525, 85320, 105995, 129766, 156849, 187460, 221815, 260130, 302621, 349504, 400995, 457310, 518665, 585276, 657359, 735130, 818805, 908600, 1004731, 1107414, 1216865, 1333300, 1456935, 1587986
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OFFSET
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0,2
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LINKS
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Euclid of Alexandria, Elements, VII Def. 17, p. 194, 300 BCE.
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FORMULA
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a(n) = 1 + 11*n + 36*n^2 + 36*n^3 = (1 + 2*n)*(1 + 3*n)*(1 + 6*n).
G.f.: (1 + 80*x + 125*x^2 + 10*x^3)/(1 - x)^4. - Stefano Spezia, Nov 29 2021
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MATHEMATICA
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nterms=50; Table[36n^3+36n^2+11n+1, {n, 0, nterms-1}] (* Paolo Xausa, Nov 25 2021 *)
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PROG
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(PARI) a(n) = subst(m*(m+1)*(m+2)/6, 'm, 6*n+1); \\ Michel Marcus, Dec 16 2021
(Python)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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