A211013 Second 13-gonal numbers: a(n) = n*(11*n+9)/2.

0, 10, 31, 63, 106, 160, 225, 301, 388, 486, 595, 715, 846, 988, 1141, 1305, 1480, 1666, 1863, 2071, 2290, 2520, 2761, 3013, 3276, 3550, 3835, 4131, 4438, 4756, 5085, 5425, 5776, 6138, 6511, 6895, 7290, 7696, 8113, 8541, 8980, 9430, 9891, 10363

Offset: 0

Author

Omar E. Pol, Aug 04 2012

Keywords

• nonn
• easy

Comments

Sequence found by reading the line from 0, in the direction 0, 31... and the line from 10, in the direction 10, 63,..., in the square spiral whose vertices are the generalized 13-gonal numbers A195313.

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).

Crossrefs

Bisection of A195313.

Second k-gonal numbers (k=5..14): A005449, A014105, A147875, A045944, A179986, A033954, A062728, A135705, this sequence, A211014.

Cf. A051865.

Programs

GAP

List([0..50], n-> n*(11*n+9)/2); # G. C. Greubel, Jul 04 2019

Magma

[n*(11*n+9)/2: n in [0..50]]; // G. C. Greubel, Jul 04 2019

Mathematica

Table[n*(11*n+9)/2, {n,0,50}] (* G. C. Greubel, Jul 04 2019 *)

PARI

a(n)=n*(11*n+9)/2 \\ Charles R Greathouse IV, Jun 17 2017

Sage

[n*(11*n+9)/2 for n in (0..50)] # G. C. Greubel, Jul 04 2019

Formula

G.f.: x*(10+x)/(1-x)^3. - Philippe Deléham, Mar 27 2013

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) with a(0) = 0, a(1) = 10, a(2) = 31. - Philippe Deléham, Mar 27 2013

a(n) = A051865(n) + 9n = A180223(n) + 8n = A022268(n) + 5n = A022269(n) + 4n = A152740(n) - n. - Philippe Deléham, Mar 27 2013

a(n) = A218530(11n+9). - Philippe Deléham, Mar 27 2013

E.g.f.: x*(20 + 11*x)*exp(x)/2. - G. C. Greubel, Jul 04 2019