A263614 a(2n) = A000125(n), a(2n+1) = 2*a(2n).

0, 0, 1, 2, 2, 4, 4, 8, 8, 16, 15, 30, 26, 52, 42, 84, 64, 128, 93, 186, 130, 260, 176, 352, 232, 464, 299, 598, 378, 756, 470, 940, 576, 1152, 697, 1394, 834, 1668, 988, 1976, 1160, 2320, 1351, 2702, 1562, 3124, 1794, 3588, 2048, 4096, 2325, 4650, 2626, 5252, 2952, 5904, 3304, 6608, 3683, 7366

Offset: 0

Author

N. J. A. Sloane, Oct 23 2015

Keywords

• nonn
• base
• easy

Comments

For n >= 2, number of palindromic squares of length n whose decimal digits are 0 or 1 and with 9 or fewer 1's.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• G. J. Simmons, Palindromic powers, J. Rec. Math., 3 (No. 2, 1970), 93-98. [Annotated scanned copy]
• Index entries for linear recurrences with constant coefficients, signature (0,4,0,-6,0,4,0,-1).

Crossrefs

Cf. A000125, A263615.

Programs

PARI

a(n) = (-((-1)^n*(-78+62*n-12*n^2+n^3))+3*(-26+42*n-8*n^2+n^3))/96 \\ Colin Barker, Oct 26 2015

PARI

concat(vector(2), Vec(x^2*(2*x+1)*(2*x^4-2*x^2+1)/((x-1)^4*(x+1)^4) + O(x^100))) \\ Colin Barker, Oct 26 2015

Formula

From Colin Barker, Oct 26 2015: (Start)

a(n) = (-((-1)^n*(-78+62*n-12*n^2+n^3))+3*(-26+42*n-8*n^2+n^3))/96.

a(n) = 4*a(n-2)-6*a(n-4)+4*a(n-6)-a(n-8) for n>7.

G.f.: x^2*(2*x+1)*(2*x^4-2*x^2+1) / ((x-1)^4*(x+1)^4).

(End)