A097657 -id:A097657 - cp's OEIS frontend

A282465 a(n) = 11*Fibonacci(n+3) + Fibonacci(n-8) with n>=0.

1, 46, 47, 93, 140, 233, 373, 606, 979, 1585, 2564, 4149, 6713, 10862, 17575, 28437, 46012, 74449, 120461, 194910, 315371, 510281, 825652, 1335933, 2161585, 3497518, 5659103, 9156621, 14815724, 23972345, 38788069, 62760414, 101548483, 164308897, 265857380, 430166277

Offset: 0

Bruno Berselli, Feb 20 2017

Similar sequences with the formula h*Fibonacci(n+k) + Fibonacci(n+k-h):
h= 1, k=-1: A000045;
h= 2, k= 1: A013655;
h= 3, k=-2: A118658 = 2*A212804;
h= 4, k= 2: A022379 = 3*A000204;
h= 5, k= 1: A022113;
h= 6, k= 2: A022125;
h= 7, k= 3: A097657;
h= 8, k= 2: A022355 = 21*A000045;
h= 9, k= 3: 10, 32, 42, 74, 116, 190, 306, 496, 802, ... =  2*A022140;
h=10, k= 3: 33, 22, 55, 77, 132, 209, 341, 550, 891, ... = 11*A013655;
h=11, k= 3: this sequence.

Indranil Ghosh, Table of n, a(n) for n = 0..4769
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (1,1).

Cf. A000045, A013655, A022113, A022125, A022355, A022379, A022379, A097657, A118658.

Cf. sequences with g.f. (1 + r*x)/(1 - x - x^2) for r = 2..31, respectively: A000204, A000285, A022095 - A022110, A022391 - A022402.

[11*Fibonacci(n+3)+Fibonacci(n-8): n in [0..40]];

Table[11 Fibonacci[n + 3] + Fibonacci[n - 8], {n, 0, 40}]
LinearRecurrence[{1,1},{1,46},36] (* or *) CoefficientList[Series[(1 + 45*x)/(1 - x - x^2) , {x,0,35}],x] (* Indranil Ghosh, Feb 22 2017 *)

a(n) = 11*fibonacci(n+3) + fibonacci(n-8) \\ Indranil Ghosh, Feb 23 2017

G.f.: (1 + 45*x)/(1 - x - x^2).
a(n) = a(n-1) + a(n-2).
a(n) = a(i)*Fibonacci(n-i+1) + a(i-1)*Fibonacci(n-i). Examples:
for i= 3,  a(3)=93,  a(2)= 47: a(n) = 93*Fibonacci(n-2) + 47*Fibonacci(n-3);
for i=-1, a(-1)=45, a(-2)=-44: a(n) = 45*Fibonacci(n+2) - 44*Fibonacci(n+1).
Other formulae:
a(n) = 44*Fibonacci(n) + Fibonacci(n+2),
a(n) = 45*Fibonacci(n) + Fibonacci(n+1),
a(n) = 46*Fibonacci(n) + Fibonacci(n-1),
a(n) = 47*Fibonacci(n) - Fibonacci(n-2).
a(n) = ((91 + sqrt(5))*((1 + sqrt(5))/2)^n - (91 - sqrt(5))*((1 - sqrt(5))/2)^n)/sqrt(20).

A098127 Fibonacci sequence with a(1) = 7 and a(2) = 26.

Original entry on oeis.org

7, 26, 33, 59, 92, 151, 243, 394, 637, 1031, 1668, 2699, 4367, 7066, 11433, 18499, 29932, 48431, 78363, 126794, 205157, 331951, 537108, 869059, 1406167, 2275226, 3681393, 5956619, 9638012, 15594631, 25232643, 40827274, 66059917, 106887191, 172947108

Offset: 1

Parthasarathy Nambi, Sep 26 2004

nonn

			a(3) = a(2) + a(1) = 26 + 7 = 33.

Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (1, 1).

Cf. A022136, A097657.

a[1]:=7:a[2]:=26: for n from 3 to 37 do a[n]:=a[n-1]+a[n-2] od: seq(a[n],n=1..37); # Emeric Deutsch, Apr 16 2005

LinearRecurrence[{1, 1}, {7, 26}, 80] (* Vladimir Joseph Stephan Orlovsky, Feb 17 2012 *)

a(n) = a(n-1) + a(n-2).

G.f.: (7x + 19x^2)/(1 - x - x^2). - Emeric Deutsch, Apr 16 2005

More terms from Emeric Deutsch, Apr 16 2005

A217762 Square array T, read by antidiagonals: T(n,k) = F(n) + 2*F(k) where F(n) is the n-th Fibonacci number.

Original entry on oeis.org

0, 2, 1, 2, 3, 1, 4, 3, 3, 2, 6, 5, 3, 4, 3, 10, 7, 5, 4, 5, 5, 16, 11, 7, 6, 5, 7, 8, 26, 17, 11, 8, 7, 7, 10, 13, 42, 27, 17, 12, 9, 9, 10, 15, 21, 68, 43, 27, 18, 13, 11, 12, 15, 23, 34, 110, 69, 43, 28, 19, 15, 14, 17, 23, 36, 55, 178, 111, 69, 44, 29, 21

Offset: 0

Philippe Deléham, Apr 07 2013

			Square array begins:
...0....2....2....4....6...10...16...26...42...
...1....3....3....5....7...11...17...27...43...
...1....3....3....5....7...11...17...27...43...
...2....4....4....6....8...12...18...28...44...
...3....5....5....7....9...13...19...29...45...
...5....7....7....9...11...15...21...31...47...
...8...10...10...12...14...18...24...34...50...
..13...15...15...17...19...23...29...39...55...
..21...23...23...25...27...31...37...47...63...
..34...36...36...38...40...44...50...60...76...
..55...57...57...59...61...65...71...81...97...
..89...91...91...93...95...99..105..115..131...
.144..146..146..148..150..154..160..170..186...
...

Cf. A000045

T(n,0) = A000045(n).
T(1,k) = A001588(k).
T(n,1) = T(n,2) = A157725(n).
T(n,3) = A157727(n).
T(n,n)= A022086(n) = 3*A000045(n).
T(n+1,n) = A000032(n+1) = A000204(n+1).
T(n+2,n) = A000285(n).
T(n+3,n) = A013655(n+1) = A001060(n+1).
T(n+4,n) = A021120(n).
T(n+5,n) = A022088(n+2) = 5*A000045(n+2).
T(n+6,n) = A022097(n+2).
T(n+7,n) = A022122(n+2).
T(n+8,n) = 3*A013655(n+2).
T(n+9,n) = A097657(n+2).
T(n+10,n) = A022118(n+4).
T(n,n+1) = A000045(n+3).
T(n,n+2) = A013655(n+1) = A001060(n+1).
T(n,n+3) = A000032(n+3).
T(n,n+4) = A022095(n+2).
T(n,n+5) = A022120(n+2).
T(n,n+6) = A022136(n+2).
T(n,n+7) = A022098(n+4).
T(n,n+8) = A022380(n+4).
T(n,n+9) = A206419(n+6).
Sum(T(n-k,k), 0<=k<=n) = 3*A000071(n+2).

cp's OEIS Frontend

A282465 a(n) = 11*Fibonacci(n+3) + Fibonacci(n-8) with n>=0.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A098127 Fibonacci sequence with a(1) = 7 and a(2) = 26.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

Extensions

A217762 Square array T, read by antidiagonals: T(n,k) = F(n) + 2*F(k) where F(n) is the n-th Fibonacci number.

Views

Author

Keywords

Examples

Crossrefs

Formula