A084604 Triangle, read by rows, where the n-th row lists the (2n+1) coefficients of (1 + x + 4x^2)^n.

1, 1, 1, 4, 1, 2, 9, 8, 16, 1, 3, 15, 25, 60, 48, 64, 1, 4, 22, 52, 145, 208, 352, 256, 256, 1, 5, 30, 90, 285, 561, 1140, 1440, 1920, 1280, 1024, 1, 6, 39, 140, 495, 1206, 2841, 4824, 7920, 8960, 9984, 6144, 4096, 1, 7, 49, 203, 791, 2261, 6027, 12489, 24108, 36176

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Example

Rows:
{1},
{1,1, 4},
{1,2, 9,  8, 16},
{1,3,15, 25, 60,  48,  64},
{1,4,22, 52,145, 208, 352, 256, 256},
{1,5,30, 90,285, 561,1140,1440,1920,1280,1024},
{1,6,39,140,495,1206,2841,4824,7920,8960,9984,6144,4096},

Mathematica

With[{eq=(1+x+4x^2)}, Flatten[Table[CoefficientList[Expand[eq^n], x], {n, 0, 10}]]] (* Harvey P. Dale, May 19 2011 *)

Prog

(PARI) for(n=0, 10, for(k=0, 2*n, t=polcoeff((1+x+4*x^2)^n, k, x); print1(t", ")); print(" "))

Crossrefs

Cf. A002426, A084600-A084603, A084605-A084615.

Sequence in context: A264922 A341030 A233528 * A152253 A280440 A024569

Adjacent sequences: A084601 A084602 A084603 * A084605 A084606 A084607

Keyword

nonn,tabf

Author

Paul D. Hanna, Jun 01 2003

Status

approved