A275277 a(n) = a(n-1) + 3*a(n-2) + 3*a(n-3) + a(n-4), where a(0) = a(1) = a(2) = a(3) = 1.

1, 1, 1, 1, 8, 15, 43, 113, 295, 778, 2045, 5377, 14141, 37185, 97784, 257139, 676187, 1778141, 4675903, 12296026, 32334345, 85028273, 223595289, 587979169, 1546184200, 4065935847, 10692021243, 28116360553, 73936416023, 194427497258, 511277848229

Offset: 0

Author

Clark Kimberling, Aug 11 2016

Keywords

• nonn
• easy

Links

• Clark Kimberling, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,3,3,1).

Crossrefs

Cf. A099234.

Programs

Mathematica

LinearRecurrence[{1, 3, 3, 1}, {1, 1, 1, 1}, 50]
RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==1,a[n]==a[n-1]+3a[n-2]+ 3a[n-3]+ a[n-4]},a,{n,30}] (* Harvey P. Dale, Apr 09 2022 *)

Formula

a(n) = a(n-1) + 3*a(n-2) + 3*a(n-3) + a(n-4), where a(0) = a(1) = a(2) = a(3) = 1.

G.f.: (-1 + 3 x^2 + 6 x^3)/(-1 + x + 3 x^2 + 3 x^3 + x^4).