login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A131253 Row sums of triangle A131252. 3
1, 3, 8, 17, 34, 64, 117, 209, 368, 641, 1108, 1904, 3257, 5551, 9432, 15985, 27030, 45616, 76845, 129245, 217056, 364033, 609768, 1020192, 1705009, 2846619, 4748072, 7912529, 13174858, 21919456, 36440613, 60538409, 100503632, 166744961, 276476092, 458151440 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (4, -4, -2, 4, 0, -1)

FORMULA

From Andrew Howroyd, Aug 09 2018: (Start)

a(n) = Sum_{k=0..n} (k+1)*(Sum_{i=0..k} binomial(n-k, k-i)).

a(n) = 4*a(n-1) - 4*a(n-2) - 2*a(n-3) + 4*a(n-4) - a(n-6).

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

(End)

EXAMPLE

a(3) = 17 = sum of row 3 terms of A131252: (7 + 6 + 3 + 1).

MATHEMATICA

LinearRecurrence[{4, -4, -2, 4, 0, -1}, {1, 3, 8, 17, 34, 64}, 40] (* Vincenzo Librandi, Aug 10 2018 *)

PROG

(PARI) Vec((1 - x - x^3)/((1 - x)^2*(1 - x - x^2)^2) + O(x^40)) \\ Andrew Howroyd, Aug 09 2018

(PARI) a(n)={sum(k=0, n, (k+1)*sum(i=0, k, binomial(n-k, k-i)))} \\ Andrew Howroyd, Aug 09 2018

(MAGMA) I:=[1, 3, 8, 17, 34, 64]; [n le 6 select I[n] else 4*Self(n-1)- 4*Self(n-2)-2*Self(n-3)+4*Self(n-4)-Self(n-6): n in [1..40]]; // Vincenzo Librandi, Aug 10 2018

CROSSREFS

Row sums of A131252.

Sequence in context: A029859 A305105 A163312 * A145071 A182734 A327608

Adjacent sequences:  A131250 A131251 A131252 * A131254 A131255 A131256

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Jun 23 2007

EXTENSIONS

Terms a(10) and beyond from Andrew Howroyd, Aug 09 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 16 12:24 EDT 2021. Contains 343943 sequences. (Running on oeis4.)