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A125129
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Partial sums of diagonals of array of k-step Lucas numbers as in A125127, read by antidiagonals.
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2
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1, 1, 4, 1, 8, 11, 1, 12, 19, 26, 1, 19, 33, 45, 57, 1, 30, 58, 84, 102, 120, 1, 48, 101, 157, 197, 222, 247, 1, 77, 179, 292, 380, 436, 469, 502, 1, 124, 318, 546, 731, 855, 929, 971, 1013, 1, 200, 567, 1026, 1409, 1674, 1838, 1932, 1984, 2036
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OFFSET
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1,3
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COMMENTS
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Array of partial sums of diagonals of L(k,n) begins: 0.|.1...4..11...26...57..120..247..502.1013.2036.
1.|.1...8..19...45..102..222..469..971.1984.
2.|.1..12..33...84..197..436..929.1932.
3.|.1..19..58..157..380..855.1838.
4.|.1..30.101..292..731.1674.
5.|.1..48.179..546.1409.
6.|.1..77.318.1026.
7.|.1.124.567.
8.|.1.200.
9.|.1.
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LINKS
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FORMULA
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Row 0 = SUM[i=1..n]L(i,i) = A127128 = partial sum of main diagonal of array of A125127. Row 1 = SUM[i=1..n]L(i,i+1) = partial sum of diagonal above main diagonal of array of A125127. Row 2 = SUM[i=1..n]L(i,i+2) = partial sum of diagonal 2 above main diagonal of array of A125127. .. Row m = SUM[i=1..n]L(i,i+m) = partial sum of diagonal 2 above main diagonal of array of A125127.
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EXAMPLE
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Row 1 of the derived array is the partial sum of the diagonal above the main diagonal of array of k-step Lucas numbers as in A125127, hence the partial sums of: 1, 7, 11, 26, 57, 120, 247, 502, 103, ... are 1 = 1; 8 = 1 + 7; 19 = 1 + 7 + 11; 45 = 1 + 7 + 11 + 26; and so forth.
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CROSSREFS
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Cf. A000012, A000032, A000204, A001644, A001648, A048887, A048888, A074048, A074584, A092921, A104621, A105754, A105755, A125127, A000295.
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KEYWORD
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AUTHOR
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STATUS
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approved
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