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A116668 a(n) = (5*n^2 + n + 2)/2. 3
1, 4, 12, 25, 43, 66, 94, 127, 165, 208, 256, 309, 367, 430, 498, 571, 649, 732, 820, 913, 1011, 1114, 1222, 1335, 1453, 1576, 1704, 1837, 1975, 2118, 2266, 2419, 2577, 2740, 2908, 3081, 3259, 3442, 3630, 3823, 4021, 4224, 4432, 4645, 4863, 5086, 5314, 5547 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of (1,3,5,0,0,0...).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

FORMULA

Product of Pascal's triangle as an infinite lower triangular matrix and the vector (1,3,5,0,0,0...)

O.g.f.: (1+x+3*x^2)/(1-x)^3. - R. J. Mathar, Apr 02 2008

a(n) = 5*n + a(n-1) - 2 (with a(0)=1) - Vincenzo Librandi, Nov 13 2010

EXAMPLE

a(3)=1*1+3*3+3*5+1*0=25.

MAPLE

a:=n->(5*n^2+n+2)/2: seq(a(n), n=0..50); # Emeric Deutsch, Feb 28 2006

MATHEMATICA

s = 1; lst = {s}; Do[s += n + 2; AppendTo[lst, s], {n, 1, 235, 5}] lst - Zerinvary Lajos, Jul 11 2009

LinearRecurrence[{3, -3, 1}, {1, 4, 12}, 50] (* G. C. Greubel, Jan 29 2018 *)

PROG

(PARI) a(n)=(5*n^2+n+2)/2 \\ Charles R Greathouse IV, Jun 17 2017

(MAGMA) [(5*n^2 + n+2)/2: n in [0..50]]; // G. C. Greubel, Jan 29 2018

(GAP) List([0..1000], n->(5*n^2+n+2)/2); # Muniru A Asiru, Jan 30 2018

CROSSREFS

Cf. A116666.

Sequence in context: A008212 A008080 A008157 * A225254 A008186 A008264

Adjacent sequences:  A116665 A116666 A116667 * A116669 A116670 A116671

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Feb 22 2006

EXTENSIONS

More terms from Emeric Deutsch, Feb 28 2006

STATUS

approved

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Last modified July 30 12:08 EDT 2021. Contains 346359 sequences. (Running on oeis4.)