A218439 a(n) = A001609(n)^2, where g.f. of A001609 is x*(1+3*x^2)/(1-x-x^3).

1, 1, 16, 25, 36, 100, 225, 441, 961, 2116, 4489, 9604, 20736, 44521, 95481, 205209, 440896, 946729, 2033476, 4368100, 9381969, 20151121, 43283241, 92968164, 199685161, 428904100, 921243904, 1978737289, 4250127249, 9128847025, 19607840784, 42115658841

Offset

1,3

Comments

A001609 equals the logarithmic derivative of Narayana's cows sequence A000930.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,3,1,-1,-1).

Formula

O.g.f.: x*(1 + 14*x^2 + 5*x^3 - 9*x^4 - 9*x^5)/((1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)).

Logarithmic derivative of A218438.

a(n) = -2*(-1)^n*A112455(n) +3*A002478(n) -2*A002478(n-1)-2*A002478(n-2), n>1. - R. J. Mathar, Oct 28 2012

Example

O.g.f.: A(x) = x + x^2 + 16*x^3 + 25*x^4 + 36*x^5 + 100*x^6 + 225*x^7 +...
L.g.f.: L(x) = x + x^2/2 + 16*x^3/3 + 25*x^4/4 + 36*x^5/5 + 100*x^6/6 + 225*x^7/7 +...
where exponentiation yields the g.f. of A218438:
exp(L(x)) = 1 + x + x^2 + 6*x^3 + 12*x^4 + 19*x^5 + 48*x^6 + 110*x^7 +...

Mathematica

Rest[CoefficientList[Series[x*(1 + 14*x^2 + 5*x^3 - 9*x^4 - 9*x^5)/((1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)), {x, 0, 50}], x]] (* G. C. Greubel, Apr 28 2017 *)

Prog

(PARI) {a(n)=polcoeff(x*(1+14*x^2+5*x^3-9*x^4-9*x^5)/((1+x^2-x^3)*(1-x-2*x^2-x^3+x*O(x^n))), n)}
for(n=1, 40, print1(a(n), ", "))

Crossrefs

Cf. A000930, A001609, A002478, A112455, A218438.

Sequence in context: A030676 A264604 A348235 * A192689 A002644 A118489

Adjacent sequences: A218436 A218437 A218438 * A218440 A218441 A218442

Keyword

nonn

Author

Paul D. Hanna, Oct 28 2012

Status

approved