OFFSET
0,2
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).
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
MATHEMATICA
Table[n*(11*n+9)/2, {n, 0, 50}] (* G. C. Greubel, Jul 04 2019 *)
PROG
(PARI) a(n)=n*(11*n+9)/2 \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [n*(11*n+9)/2: n in [0..50]]; // G. C. Greubel, Jul 04 2019
(Sage) [n*(11*n+9)/2 for n in (0..50)] # G. C. Greubel, Jul 04 2019
(GAP) List([0..50], n-> n*(11*n+9)/2) # G. C. Greubel, Jul 04 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Aug 04 2012
STATUS
approved