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Search: id:A125129
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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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+0
3
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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
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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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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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, ... =
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, A125128.
Sequence in context: A105533 A124848 A090219 this_sequence A013611 A077910 A100235
Adjacent sequences: A125126 A125127 A125128 this_sequence A125130 A125131 A125132
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Nov 23 2006
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