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%I A125129 #8 May 01 2013 08:56:49
%S A125129 1,1,4,1,8,11,1,12,19,26,1,19,33,45,57,1,30,58,84,102,120,1,48,101,
%T A125129 157,197,222,247,1,77,179,292,380,436,469,502,1,124,318,546,731,855,
%U A125129 929,971,1013,1,200,567,1026,1409,1674,1838,1932,1984,2036
%N A125129 Partial sums of diagonals of array of k-step Lucas numbers as in A125127, read by antidiagonals.
%C A125129 Array of partial sums of diagonals of L(k,n) begins: 0.|.1...4..11...26...57..120..247..502.1013.2036.
%C A125129   1.|.1...8..19...45..102..222..469..971.1984.
%C A125129   2.|.1..12..33...84..197..436..929.1932.
%C A125129   3.|.1..19..58..157..380..855.1838.
%C A125129   4.|.1..30.101..292..731.1674.
%C A125129   5.|.1..48.179..546.1409.
%C A125129   6.|.1..77.318.1026.
%C A125129   7.|.1.124.567.
%C A125129   8.|.1.200.
%C A125129   9.|.1.
%F A125129 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.
%e A125129 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.
%Y A125129 Cf. A000012, A000032, A000204, A001644, A001648, A048887, A048888, A074048, A074584, A092921, A104621, A105754, A105755, A125127, A000295.
%K A125129 easy,nonn,tabl
%O A125129 1,3
%A A125129 _Jonathan Vos Post_, Nov 23 2006

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