A262000 a(n) = n^2*(7*n - 5)/2.

0, 1, 18, 72, 184, 375, 666, 1078, 1632, 2349, 3250, 4356, 5688, 7267, 9114, 11250, 13696, 16473, 19602, 23104, 27000, 31311, 36058, 41262, 46944, 53125, 59826, 67068, 74872, 83259, 92250, 101866, 112128, 123057, 134674, 147000, 160056, 173863, 188442, 203814, 220000

Offset

0,3

Comments

Also, structured enneagonal prism numbers.

Links

Bruno Berselli, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

G.f.: x*(1 + 14*x + 6*x^2)/(1 - x)^4.

a(n) = Sum_{i=0..n-1} n*(7*i+1) for n>0, a(0)=0.

a(n+1) + a(-n) = A069125(n+1).

Sum_{i>0} 1/a(i) = 1.082675669875907610300284768825... = (42*(log(14) + 2*(cos(Pi/7)*log(cos(3*Pi/14)) + log(sin(Pi/7))*sin(Pi/14) - log(cos(Pi/14)) * sin(3*Pi/14))) + 21*Pi*tan(3*Pi/14))/75 - Pi^2/15. - Vaclav Kotesovec, Oct 04 2016

Example

For n=8, a(8) = 8*(7*0+1)+8*(7*1+1)+8*(7*2+1)+8*(7*3+1)+8*(7*4+1)+8*(7*5+1)+8*(7*6+1)+8*(7*7+1) = 1632.

Mathematica

Table[n^2 (7 n - 5)/2, {n, 0, 40}]
LinearRecurrence[{4, -6, 4, -1}, {0, 1, 18, 72}, 50] (* Harvey P. Dale, Oct 04 2016 *)

Prog

(PARI) vector(40, n, n--; n^2*(7*n-5)/2)
(Sage) [n^2*(7*n-5)/2 for n in (0..40)]
(Magma) [n^2*(7*n-5)/2: n in [0..40]];

Crossrefs

Cf. similar sequences with the formula n^2*(k*n-k+2)/2: A000290 (k=0), A002411 (k=1), A000578 (k=2), A050509 (k=3), A015237 (k=4), A006597 (k=5), A100176 (k=6), this sequence (k=7), A103532 (k=8).

Cf. A001106, A069125.

Sequence in context: A373903 A195321 A069058 * A007276 A052619 A110753

Adjacent sequences: A261997 A261998 A261999 * A262001 A262002 A262003

Keyword

nonn,easy

Author

Bruno Berselli, Sep 08 2015

Status

approved