A138476 Triangle read by rows: expansion of (1 + 3*x^2)/(1 - x*(2*y-x)).

1, 0, 2, 2, 0, 4, 0, 2, 0, 8, -2, 0, 0, 0, 16, 0, -6, 0, -8, 0, 32, 2, 0, -12, 0, -32, 0, 64, 0, 10, 0, -16, 0, -96, 0, 128, -2, 0, 32, 0, 0, 0, -256, 0, 256, 0, -14, 0, 80, 0, 96, 0, -640, 0, 512, 2, 0, -60, 0, 160, 0, 448, 0, -1536, 0, 1024, 0, 18, 0, -200, 0, 224, 0, 1536, 0, -3584, 0, 2048

Offset

0,3

Comments

See A135929 and A138034 for further information.

References

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972; see Chapter 22.

Links

Table of n, a(n) for n=0..77.

Formula

G.f.: (1 + 3*x^2)/(1 - x*(2*y-x)).

Example

Triangle begins:
   1;
   0,  2;
   2,  0,   4;
   0,  2,   0,   8;
  -2,  0,   0,   0,  16;
   0, -6,   0,  -8,   0,  32;
   2,  0, -12,   0, -32,   0,   64;
   0, 10,   0, -16,   0, -96,    0, 128;
  -2,  0,  32,   0,   0,   0, -256,   0, 256;
  ...

Prog

(PARI) T(n)=[Vecrev(p) | p<-Vec((1 + 3*x^2)/(1 - x*(2*y-x)) + O(x*x^n))]
{ my(A=T(10)); for(i=1, #A, print(A[i])) }

Crossrefs

Row sums are A111284(n+1).

Main diagonal is A000079.

Sequence in context: A167001 A108563 A378982 * A131381 A295215 A112080

Adjacent sequences: A138473 A138474 A138475 * A138477 A138478 A138479

Keyword

tabl,sign

Author

A. Bannour (managing_office069(AT)yahoo.fr), Mar 19 2008

Extensions

New name from Joerg Arndt, May 15 2016

Offset changed and more terms from Andrew Howroyd, Oct 31 2025

a(14) and some following terms corrected by Georg Fischer, May 09 2026

Status

approved