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

Author

Clark Kimberling

Keywords

• nonn

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).

Crossrefs

Cf. A026998, A122514.

Programs

Magma

R:= 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

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 *)

SageMath

def A027010_list(prec):
    P. = 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

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