A190090 Diagonal sums of the triangular matrix A190088.

1, 1, 4, 16, 42, 137, 443, 1365, 4316, 13625, 42785, 134758, 424331, 1335378, 4203927, 13233947, 41657808, 131135696, 412803240, 1299458257, 4090567673, 12876698159, 40534529294, 127598621869, 401667591501, 1264408966284, 3980231826575, 12529367967276, 39441185140197

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..201

Index entries for linear recurrences with constant coefficients, signature (2,2,6,-3,0,1).

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(3*n-4*k+1,3*n-6*k+1).

G.f.: (1-x-x^4)/(1-2*x-2*x^2-6*x^3+3*x^4-x^6).

a(n) = 2*a(n-1)+ 2*a(n-2)+ 6*a(n-3)-3*a(n-4)+a(n-6), and a(0)=1, a(1)=1, a(2)=4, a(3)=16, a(4)=42, a(5)=137, . - Harvey P. Dale, Jul 04 2011

Mathematica

Table[Sum[Binomial[3n - 4k + 1, 3n - 6k + 1], {k, 0, n/2}], {n, 0, 26}]
LinearRecurrence[{2, 2, 6, -3, 0, 1}, {1, 1, 4, 16, 42, 137}, 27] (* Harvey P. Dale, Jul 04 2011 *)

Prog

(Maxima) makelist(sum(binomial(3*n-4*k+1, 3*n-6*k+1), k, 0, n/2), n, 0, 12);
(PARI) Vec((1-x-x^4)/(1-2*x-2*x^2-6*x^3+3*x^4-x^6)+O(x^29)) \\ Charles R Greathouse IV, Jun 30 2011
(Magma) [(&+[Binomial(3*n-4*k+1, 3*n-6*k+1): k in [0..Floor(n/2)]]): n in [0..30]]; // G. C. Greubel, Mar 04 2018

Crossrefs

Cf. A190088, A190089.

Sequence in context: A114211 A188124 A344857 * A227012 A034131 A183536

Adjacent sequences: A190087 A190088 A190089 * A190091 A190092 A190093

Keyword

nonn,easy

Author

Emanuele Munarini, May 04 2011

Status

approved