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A235332
a(n) = n*(9*n + 25)/2 + 6.
8
6, 23, 49, 84, 128, 181, 243, 314, 394, 483, 581, 688, 804, 929, 1063, 1206, 1358, 1519, 1689, 1868, 2056, 2253, 2459, 2674, 2898, 3131, 3373, 3624, 3884, 4153, 4431, 4718, 5014, 5319, 5633, 5956, 6288, 6629, 6979, 7338, 7706, 8083, 8469, 8864, 9268, 9681, 10103
OFFSET
0,1
COMMENTS
This is the case d=6 of n*(9*n + 4*d + 1)/2 + d. Other similar sequences are:
d=0, A022267;
d=1, A064225;
d=2, A062123;
d=3, A064226;
d=4, A022266 (with initial 0);
d=5, A178977.
First bisection of A235537.
FORMULA
G.f.: (6 + 5*x - 2*x^2)/(1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
2*a(n) - a(n+1) + 12 = A081267(n).
E.g.f.: exp(x)*(12 + 34*x + 9*x^2)/2. - Elmo R. Oliveira, Nov 13 2024
MATHEMATICA
Table[n (9 n + 25)/2 + 6, {n, 0, 50}]
LinearRecurrence[{3, -3, 1}, {6, 23, 49}, 50] (* Harvey P. Dale, Feb 12 2022 *)
PROG
(Magma) [n*(9*n+25)/2+6: n in [0..50]];
(PARI) a(n)=n*(9*n+25)/2+6 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
Sequence in context: A031293 A250647 A304392 * A026817 A022269 A212570
KEYWORD
nonn,easy,changed
AUTHOR
Bruno Berselli, Jan 22 2014
STATUS
approved