A027010 a(n) = Sum_{k=floor((n+1)/2)..n} T(k,n-k); i.e., a(n) is the n-th diagonal sum of left-justified array T given by A026998.

1, 1, 2, 5, 6, 13, 17, 29, 43, 64, 100, 144, 223, 326, 492, 733, 1089, 1634, 2421, 3626, 5389, 8041, 11985, 17847, 26624, 39640, 59112, 88059, 131242, 195592, 291433, 434369, 647218, 964581, 1437374, 2142013, 3192113, 4756821

Offset

1,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,2,-1,-2,1).

Formula

G.f.: x*(1 - x^2 + 2*x^3)/((1-x)*(1-2*x^2-x^3+x^4)).

a(n) = 2*b(n+2) + 3*b(n+1) - b(n) - 4*b(n-1) - 2, where b(n) = A122514(n). - G. C. Greubel, Jul 11 2025

Mathematica

CoefficientList[Series[(1-x^2+2 x^3)/((1-x)(1-2 x^2 -x^3 +x^4)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 03 2017 *)

Prog

(Magma)
R<x>:= PowerSeriesRing(Integers(), 40);
Coefficients(R!( x*(1-x^2+2*x^3)/((1-x)*(1-2*x^2-x^3+x^4)) )); // G. C. Greubel, Jul 11 2025
(SageMath)
def A027010_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( x*(1-x^2+2*x^3)/((1-x)*(1-2*x^2-x^3+x^4)) ).list()
a=A027010_list(40); a[1:] # G. C. Greubel, Jul 11 2025
(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 1, -2, -1, 2, 1]^(n-1)*[1; 1; 2; 5; 6])[1, 1] \\ Charles R Greathouse IV, May 29 2026

Crossrefs

Cf. A026998, A122514.

Sequence in context: A325285 A323348 A181314 * A038191 A321472 A087128

Adjacent sequences: A027007 A027008 A027009 * A027011 A027012 A027013

Keyword

nonn,easy,changed

Author

Clark Kimberling

Status

approved