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A190090 Diagonal sums of the triangular matrix A190088. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A323847 A114211 A188124 * A227012 A034131 A183536

Adjacent sequences:  A190087 A190088 A190089 * A190091 A190092 A190093

KEYWORD

nonn,easy

AUTHOR

Emanuele Munarini, May 04 2011

STATUS

approved

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Last modified September 20 03:55 EDT 2019. Contains 327212 sequences. (Running on oeis4.)