A034859 a(n) = C(n+3,4) + 3*C(n+1,3) + 5*C(n-1,2) + 7*n - 15 for n >= 3; a(1)=1, a(2)=10.

1, 10, 38, 93, 180, 308, 487, 728, 1043, 1445, 1948, 2567, 3318, 4218, 5285, 6538, 7997, 9683, 11618, 13825, 16328, 19152, 22323, 25868, 29815, 34193, 39032, 44363, 50218, 56630, 63633, 71262, 79553

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

G.f.: (1+5*z-2*z^2-7*z^3+7*z^5-3*z^6)*z/(1-z)^5. - Robert Israel, Jun 14 2017

Maple

1, 10, seq(binomial(n+3, 4)+3*binomial(n+1, 3)+5*binomial(n-1, 2)+7*n-15, n=3..40);
# Robert Israel, Jun 14 2017

Mathematica

Join[{1, 10}, Table[Binomial[n+3, 4]+3Binomial[n+1, 3]+5Binomial[n-1, 2]+7n-15, {n, 3, 40}]] (* Harvey P. Dale, Jan 09 2014 *)

Prog

(PARI) x='x+O('x^30); Vec(x*(1+5*x-2*x^2-7*x^3+7*x^5-3*x^6)/(1-x)^5) \\ G. C. Greubel, Feb 22 2018
(Magma) [1, 10] cat [Binomial(n+3, 4) + 3*Binomial(n+1, 3) + 5*Binomial(n-1, 2) + 7*n -15: n in [3..30]]; // G. C. Greubel, Feb 22 2018

Crossrefs

Sequence in context: A065009 A031430 A154517 * A197060 A257051 A250420

Adjacent sequences: A034856 A034857 A034858 * A034860 A034861 A034862

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved