A195837 - OEIS

%I #18 Mar 30 2012 17:34:07

%S 1,1,1,1,1,2,1,3,1,4,1,-1,4,2,-1,5,3,-1,7,4,-1,10,4,-2,12,5,-3,14,7,

%T -4,-1,16,10,-4,-1,21,12,-5,-1,27,14,-7,-1,33,16,-10,-2,37,21,-12,-3,

%U 1,44,27,-14,-4,1,54,33,-16,-4,1,68,37,-21,-5,1,80,44,-27,-7,2

%N Triangle read by rows which arises from A195827, in the same way as A175003 arises from A195310. Column k starts at row A085787(k).

%C The sum of terms of row n is equal to the leftmost term of row n+1. It appears that this sequence is related to the generalized heptagonal numbers A085787, A195827 and A036820 in the same way as A175003 is related to the generalized pentagonal numbers A001318, A195310 and A000041. It appears that row sums give A036820. See comments in A195825.

%e Written as a triangle:

%e .  1;

%e .  1;

%e .  1;

%e .  1,   1;

%e .  2,   1;

%e .  3,   1;

%e .  4,   1,  -1;

%e .  4,   2,  -1;

%e .  5,   3,  -1;

%e .  7,   4,  -1;

%e . 10,   4,  -2;

%e . 12,   5,  -3;

%e . 14,   7,  -4,  -1;

%e . 16,  10,  -4,  -1;

%e . 21,  12,  -5,  -1;

%e . 27,  14,  -7,  -1;

%e . 33,  16, -10,  -2;

%e . 37,  21, -12,  -3,  1;

%e . 44,  27, -14,  -4,  1;

%e . 54,  33, -16,  -4,  1;

%Y Cf. A085787, A036820, A175003, A195825, A195826, A195827, A195836, A195838, A195839, A195840, A195841, A195842, A195843.

%K sign,tabf

%O 1,6

%A _Omar E. Pol_, Sep 24 2011