A105524 Diagonal sums of number triangle A105522.

1, -2, 2, 0, -1, -2, 4, 4, -10, -12, 30, 36, -93, -114, 300, 372, -994, -1244, 3364, 4240, -11578, -14676, 40400, 51448, -142592, -182288, 508166, 651756, -1826037, -2348562, 6608844, 8520564, -24069258, -31097388, 88145436, 114096096, -324391422, -420590652, 1199074584

Offset

0,2

Links

Table of n, a(n) for n=0..38.

Formula

G.f.: ((1+2x)sqrt(1+4x^2)-4x^2-2x-1)/(x^2*(sqrt(1+4x^2)-3)). - amended by Georg Fischer, Apr 09 2020

Conjecture: 2*(n+2)*(13*n^2-35*n+6)*a(n) +24*(n-8)*a(n-1) +(91*n^3-375*n^2+152*n+372)*a(n-2) +12*(8-n)*a(n-3) -4*(n-3)*(13*n^2-9*n-16)*a(n-4) = 0. - R. J. Mathar, Nov 09 2012

Mathematica

CoefficientList[Series[((1+2*x)*Sqrt[1+4*x^2]-4*x^2-2*x-1)/(x^2*(Sqrt[1+4*x
^2]-3)), {x, 0, 30}], x] (* Georg Fischer, Apr 09 2020 *)

Crossrefs

Sequence in context: A306706 A163000 A303548 * A221459 A166387 A000209

Adjacent sequences: A105521 A105522 A105523 * A105525 A105526 A105527

Keyword

easy,sign

Author

Paul Barry, Apr 13 2005

Status

approved