A276288 a(n) = a(n-1) + 3*a(n-2) if n is even, otherwise a(n) = 3*a(n-1) + a(n-2), a(0)=0, a(1)=1.

0, 1, 1, 4, 7, 25, 46, 163, 301, 1066, 1969, 6973, 12880, 45613, 84253, 298372, 551131, 1951765, 3605158, 12767239, 23582713, 83515378, 154263517, 546305929, 1009096480, 3573595369, 6600884809, 23376249796, 43178904223, 152912962465, 282449675134, 1000261987867, 1847611013269, 6543095027674

Offset

0,4

Links

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (0,7,0,-3).

Formula

G.f.: x*(1 + x - 3*x^2)/(1 - 7*x^2 + 3*x^4).

a(n) = 7*a(n-2) - 3*a(n-4).

a(n) = (2 - (-1)^n)*a(n-1) + (2 + (-1)^n)*a(n-2) for n > 1, a(0)=0, a(1)=1.

a(2k) = A190972(k).

Mathematica

LinearRecurrence[{0, 7, 0, -3}, {0, 1, 1, 4}, 34]
RecurrenceTable[{a[0] == 0, a[1] == 1, a[n] == (2 - (-1)^n) a[n - 1] + (2 + (-1)^n) a[n - 2]}, a, {n, 33}]

Prog

(PARI) concat(0, Vec(x*(1+x-3*x^2)/(1-7*x^2+3*x^4) + O(x^99))) \\ Altug Alkan, Aug 27 2016

Crossrefs

Cf. A005824, A010684, A079162, A190972.

Sequence in context: A129418 A372169 A073218 * A219700 A151348 A211942

Adjacent sequences: A276285 A276286 A276287 * A276289 A276290 A276291

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Aug 27 2016

Status

approved