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A022265 a(n) = n*(7*n + 1)/2. 10
0, 4, 15, 33, 58, 90, 129, 175, 228, 288, 355, 429, 510, 598, 693, 795, 904, 1020, 1143, 1273, 1410, 1554, 1705, 1863, 2028, 2200, 2379, 2565, 2758, 2958, 3165, 3379, 3600, 3828, 4063, 4305, 4554, 4810 (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) = A110449(n, 3) for n>2.

a(n) = A049453(n) - A005475(n). - Zerinvary Lajos, Jan 21 2007

a(n) = 7*n + a(n-1) - 3 for n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) with a(0)=0, a(1)=4, a(2)=15. - Philippe Deléham, Mar 26 2013

a(n) = A174738(7n+3). - Philippe Deléham, Mar 26 2013

a(n) = A000217(4*n) - A000217(3*n). - Bruno Berselli, Oct 13 2016

G.f.: x*(4 + 3*x)/(1 - x)^3. - Ilya Gutkovskiy, Oct 13 2016

E.g.f.: (x/2)*(7*x + 8)*exp(x). - G. C. Greubel, Aug 23 2017

EXAMPLE

From Bruno Berselli, Oct 27 2017: (Start)

After 0:

4  =       -(1)       +             (2 + 3).

15 =     -(1 + 2)     +         (3 + 4 + 5 + 6).

33 =   -(1 + 2 + 3)   +     (4 + 5 + 6 + 7 + 8 + 9).

58 = -(1 + 2 + 3 + 4) + (5 + 6 + 7 + 8 + 9 + 10 + 11 + 12). (End)

MAPLE

seq(binomial(7*n+1, 2)/7, n=0..37); # Zerinvary Lajos, Jan 21 2007

seq(binomial(6*n+1, 2)/3-binomial(5*n+1, 2)/5, n=0..42); # Zerinvary Lajos, Jan 21 2007

MATHEMATICA

Table[n (7 n + 1)/2, {n, 0, 40}] (* Bruno Berselli, Oct 13 2016 *)

PROG

(PARI) a(n)=n*(7*n+1)/2 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A001106, A022264, A024966, A110449, A174738, A179986, A186029, A218471.

Cf. similar sequences listed in A022289.

Sequence in context: A110341 A116035 A256715 * A120389 A124150 A054556

Adjacent sequences:  A022262 A022263 A022264 * A022266 A022267 A022268

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 18 14:15 EST 2017. Contains 294893 sequences.