A125129 Partial sums of diagonals of array of k-step Lucas numbers as in A125127, read by antidiagonals.

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

Offset

1,3

Comments

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.

Links

Table of n, a(n) for n=1..55.

Formula

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.

Example

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.

Crossrefs

Cf. A000012, A000032, A000204, A001644, A001648, A048887, A048888, A074048, A074584, A092921, A104621, A105754, A105755, A125127, A000295.

Sequence in context: A124848 A090219 A264285 * A324780 A280108 A299583

Adjacent sequences: A125126 A125127 A125128 * A125130 A125131 A125132

Keyword

easy,nonn,tabl

Author

Jonathan Vos Post, Nov 23 2006

Status

approved