A170975 Expansion of Product_{i=0..m-1} (1 + x^(4*i+1)) for m = 12.

1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 3, 2, 0, 1, 3, 3, 1, 1, 4, 4, 1, 1, 4, 5, 2, 1, 5, 7, 3, 1, 5, 8, 5, 2, 6, 10, 6, 1, 5, 12, 9, 2, 5, 13, 11, 3, 4, 14, 15, 5, 4, 15, 17, 7, 4, 15, 21, 10, 4, 15, 23, 13, 4, 15, 27, 17, 5, 14, 28, 21, 6, 13, 31, 26, 8, 12, 31, 30, 11, 11

Offset: 0

Author

N. J. A. Sloane, Aug 29 2010

Keywords

• nonn
• fini
• full
• easy

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..276 (full sequence)

Crossrefs

Cf. A169975, A170966-A170984.

Programs

Magma

m:=12; R:=PowerSeriesRing(Integers(), 100); Coefficients(R!( (&*[1+x^(4*j+1): j in [0..m-1]]) )); // G. C. Greubel, Feb 24 2019

Maple

seq(coeff(mul((1+x^(4*i+1)),i=0..11),x,n),n=0..100); # Nathaniel Johnston, Jun 24 2011

Mathematica

With[{m=12}, CoefficientList[Series[Product[(1 + x^(4*j+1)), {j,0,m-1}], {x,0,100}],x]] (* G. C. Greubel, Feb 24 2019 *)

PARI

m=12; my(x='x+O('x^(100))); Vec(prod(j=0,m-1, 1+x^(4*j+1) )) \\ G. C. Greubel, Feb 24 2019

Sage

m=12; ( prod(1+x^(4*j+1) for j in (0..m-1)) ).series(x, 100).coefficients(x, sparse=False) # G. C. Greubel, Feb 24 2019

Formula

a(n) = a(276-n). - Rick L. Shepherd, Mar 01 2013

Extensions

Typo in Maple program fixed and b-file extended 9 terms by Rick L. Shepherd, Mar 01 2013