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A140674 a(n) = n*(3*n + 17)/2. 12
0, 10, 23, 39, 58, 80, 105, 133, 164, 198, 235, 275, 318, 364, 413, 465, 520, 578, 639, 703, 770, 840, 913, 989, 1068, 1150, 1235, 1323, 1414, 1508, 1605, 1705, 1808, 1914, 2023, 2135, 2250, 2368, 2489, 2613, 2740, 2870, 3003, 3139 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

a(n) = (3*n^2 + 17*n)/2.

a(n) = 7*n + 3*A000217(n). - Reinhard Zumkeller, May 28 2008

a(n) = 3*n + a(n-1) + 7 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010

G.f.: x*(10 - 7*x)/(1 - x)^3. - Arkadiusz Wesolowski, Dec 24 2011

E.g.f.: (1/2)*(3*x^2 + 20*x)*exp(x). - G. C. Greubel, Jul 17 2017

EXAMPLE

a(1)=3*1+0+7=10; a(2)=3*2+10+7=23; a(3)=3*3+23+7=39. - Vincenzo Librandi, Aug 03 2010

MAPLE

with(finance):seq(add(cashflows([2, k, n], 0 ), k=4..n), n=3..46); # Zerinvary Lajos, Jun 22 2008

MATHEMATICA

s=0; lst={s}; Do[s+=n++ +10; AppendTo[lst, s], {n, 0, 7!, 3}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 17 2008 *)

Table[(3*n^2 + 17*n)/2, {n, 0, 50}] (* G. C. Greubel, Jul 17 2017 *)

PROG

(PARI) a(n)=n*(3*n+17)/2 \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

The generalized pentagonal numbers b*n+3*n*(n-1)/2, for b = 1 through 12, form sequences A000326, A005449, A045943, A115067, A140090, A140091, A059845, A140672, A140673, A140674, A140675, A151542.

Sequence in context: A125618 A154033 A275238 * A072245 A135277 A156202

Adjacent sequences:  A140671 A140672 A140673 * A140675 A140676 A140677

KEYWORD

easy,nonn

AUTHOR

Omar E. Pol, May 22 2008

STATUS

approved

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Last modified April 21 21:03 EDT 2018. Contains 302877 sequences. (Running on oeis4.)