A134816 -id:A134816 - cp's OEIS frontend

A376647 a(n) = Sum_{k=0..floor(n/3)} binomial(floor(k/2),n-3*k).

1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 2, 1, 1, 2, 1, 1, 3, 3, 2, 3, 3, 2, 4, 6, 5, 5, 6, 5, 6, 10, 11, 10, 11, 11, 11, 16, 21, 21, 21, 22, 22, 27, 37, 42, 42, 43, 44, 49, 64, 79, 84, 85, 87, 93, 113, 143, 163, 169, 172, 180, 206, 256, 306, 332, 341, 352, 386, 462, 562

Offset: 0

Seiichi Manyama, Oct 01 2024

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1,1).

Cf. A124789, A134816, A376648.

Cf. A017847.

a(n) = sum(k=0, n\3, binomial(k\2, n-3*k));

my(N=80, x='x+O('x^N)); Vec((1+x^3)/(1-x^6-x^7))

G.f.: (1-x^6)/((1-x^3) * (1-x^6-x^7)) = (1+x^3)/(1-x^6-x^7).
a(n) = a(n-6) + a(n-7).
a(n) = A017847(n) + A017847(n-3).

A376648 a(n) = Sum_{k=0..floor(n/4)} binomial(floor(k/2),n-4*k).

Original entry on oeis.org

1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 3, 3, 1, 1, 3, 3, 1, 1, 4, 6, 4, 2, 4, 6, 4, 2, 5, 10, 10, 6, 6, 10, 10, 6, 7, 15, 20, 16, 12, 16, 20, 16, 13, 22, 35, 36, 28, 28, 36, 36, 29, 35, 57, 71, 64, 56, 64, 72, 65, 64, 92, 128, 135

Offset: 0

Seiichi Manyama, Oct 01 2024

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1,1).

Cf. A124789, A134816, A376647.

Cf. A017867.

a(n) = sum(k=0, n\4, binomial(k\2, n-4*k));

my(N=80, x='x+O('x^N)); Vec((1+x^4)/(1-x^8-x^9))

G.f.: (1-x^8)/((1-x^4) * (1-x^8-x^9)) = (1+x^4)/(1-x^8-x^9).
a(n) = a(n-8) + a(n-9).
a(n) = A017867(n) + A017867(n-4).

A276275 Padovan like sequence: a(n) = a(n-2) + a(n-3) for n>3, a(1)=2, a(2)=2, a(3)=0.

Original entry on oeis.org

2, 2, 0, 4, 2, 4, 6, 6, 10, 12, 16, 22, 28, 38, 50, 66, 88, 116, 154, 204, 270, 358, 474, 628, 832, 1102, 1460, 1934, 2562, 3394, 4496, 5956, 7890, 10452, 13846, 18342, 24298, 32188, 42640, 56486, 74828, 99126, 131314, 173954, 230440, 305268, 404394, 535708

Offset: 1

Nicolas Bègue, Aug 26 2016

Obtained from Padovan Spiral number (A134816) modulo 3 reduction periodic sequence 1112201210010, 111 112 122 220 ... fourth initialization values 220, it satisfies the same recurrence a(n) = a(n-2) + a(n-3).

Index entries for linear recurrences with constant coefficients, signature (0,1,1).

Cf. A134816, A084338.

RecurrenceTable[{a[n] == a[n - 2] + a[n - 3], a[1] == 2, a[2] == 2, a[3] == 0}, a, {n, 1, 48}] (* or *) CoefficientList[Series[2 x (1 + x - x^2)/(1 - x^2 - x^3), {x, 0, 47}], x] (* Michael De Vlieger, Sep 02 2016 *)
LinearRecurrence[{0,1,1},{2,2,0},60] (* Harvey P. Dale, Jan 27 2023 *)

G.f.: 2*x*(1 + x - x^2)/(1 - x^2 - x^3).
a(n) = A134816(n) + A007307(n-3) for n>=4.
a(n) = 2*A084338(n-3) for n>=4.

cp's OEIS Frontend

A376647 a(n) = Sum_{k=0..floor(n/3)} binomial(floor(k/2),n-3*k).

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A376648 a(n) = Sum_{k=0..floor(n/4)} binomial(floor(k/2),n-4*k).

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A276275 Padovan like sequence: a(n) = a(n-2) + a(n-3) for n>3, a(1)=2, a(2)=2, a(3)=0.

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