A173277 A(x) satisfies A000290(x)/x^2 = A(x)/A(x^2); A000290 = integer squares

1, 4, 13, 32, 74, 152, 298, 544, 964, 1632, 2700, 4320, 6790, 10408, 15718, 23264, 34010, 48920, 69626, 97760, 136022, 187112, 255350, 345056, 463020, 616032, 814500, 1068832, 1394746, 1807960, 2331738, 2989344, 3814788, 4842080, 6120140, 7697888, 9644950

Offset

1,2

Links

Table of n, a(n) for n=1..37.

Formula

A(x) = (1+x)*A(x^2)/(x*(1-x)^3).

Given triangle A152205, (squares in every column shifted down twice) = M, then

Lim_{n->inf} M^n = A173277 as a left-shifted vector.

Example

(1 + 4x + 13x^2 + 32x^3 + ...) = (1 + 4x + 9x^2 + 16x^3 + ...)
/ (1 + 4x^2 + 9x^4 + 16x^6 + ...)= (1, 4, 13, 32,...) = (1, 4, 9, 16,...)
/ (1, 0, 4, 0, 9, 0, 16,...).

Crossrefs

Cf. A000290, A152205

Sequence in context: A051912 A060099 A208638 * A036420 A266094 A054039

Adjacent sequences: A173274 A173275 A173276 * A173278 A173279 A173280

Keyword

nonn

Author

Gary W. Adamson, Feb 14 2010

Extensions

Definition corrected to match the offset by R. J. Mathar, Feb 21 2010

Status

approved