A000383 -id:A000383 - cp's OEIS frontend

A214830 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 8.

1, 8, 8, 17, 33, 58, 108, 199, 365, 672, 1236, 2273, 4181, 7690, 14144, 26015, 47849, 88008, 161872, 297729, 547609, 1007210, 1852548, 3407367, 6267125, 11527040, 21201532, 38995697, 71724269, 131921498, 242641464, 446287231, 820850193, 1509778888

Offset: 0

Abel Amene, Aug 07 2012

See comments in A214727.

Robert Price, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,1).

Cf. A000213, A000288, A000322, A000383, A060455, A136175, A141036, A141523, A214825-A214831.

a:=[1,8,8];; for n in [4..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]; od; a; # G. C. Greubel, Apr 24 2019

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+7*x-x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 24 2019

CoefficientList[Series[(x^2-7*x-1)/(x^3+x^2+x-1), {x, 0, 40}], x] (* Wesley Ivan Hurt, Jun 18 2014 *)
LinearRecurrence[{1,1,1}, {1,8,8}, 40] (* G. C. Greubel, Apr 24 2019 *)

my(x='x+O('x^40)); Vec((1+7*x-x^2)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 24 2019

((1+7*x-x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 24 2019

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

a(n) = -A000073(n) + 7*A000073(n+1) + A000073(n+2). - G. C. Greubel, Apr 24 2019

A253318 Indices of primes in the 7th-order Fibonacci number sequence, A060455.

Original entry on oeis.org

7, 8, 11, 12, 14, 15, 16, 17, 18, 19, 21, 23, 26, 32, 33, 36, 42, 44, 71, 72, 137, 180, 193, 285, 679, 955, 1018, 1155, 1176, 1191, 2149, 2590, 2757, 3364, 4233, 6243, 6364, 7443, 10194, 11254, 13318, 18995, 20478, 22647, 29711, 34769, 61815, 71993, 107494, 135942, 148831

Offset: 1

Robert Price, Dec 30 2014

nonn

a(52) > 2*10^5.

Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4

Cf. A001590, A001631, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523, A214825, A235862, A000288, A000322, A000383, A249413, A060455.

a={1,1,1,1,1,1,1}; step=7; lst={}; For[n=step,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,n]]; a=RotateLeft[a]; a[[7]]=sum]; lst

A061451 Array T(n,k) of k-th order Fibonacci numbers read by antidiagonals in up-direction.

Original entry on oeis.org

2, 3, 3, 4, 5, 5, 5, 7, 9, 8, 6, 9, 13, 17, 13, 7, 11, 17, 25, 31, 21, 8, 13, 21, 33, 49, 57, 34, 9, 15, 25, 41, 65, 94, 105, 55, 10, 17, 29, 49, 81, 129, 181, 193, 89, 11, 19, 33, 57, 97, 161, 253, 349, 355, 144, 12, 21, 37, 65, 113, 193, 321, 497, 673, 653, 233

Offset: 1

Frank Ellermann, Jun 11 2001

			2, 3, 5, 8 ... first order, a(1)=2, a(3)=3, a(6)=5, a(10)=8, ...
3, 5, 9,17 ... 2nd order, a(2)=3, a(5)=5, a(9)=9, ...
4, 7,13,25 ... 3rd order, a(4)=4, a(8)=7, ...
5, 9,17,33 ... 4th order, a(7)=5, ...

N. Wirth, Algorithmen und Datenstrukturen, 1975, table 2.15 (ch. 2.3.4)

T. D. Noe, Rows n=1..50 of triangle, flattened

Rows 1..6: A000045, A000213, A000288, A000322, A000383, A060455.

max = 12; Clear[f]; f[k_, n_] /; n > k := f[k, n] = Sum[f[k, n - j], {j, 1, k + 1}]; f[k_, n_] = 1; t = Table[ Table[ f[k, n], {n, k + 1, max}], {k, 1, max}]; Table[ t[[k - n + 1, n]], {k, 1, max - 1}, {n, 1, k}] // Flatten (* Jean-François Alcover, Apr 10 2013 *)

A253705 Indices of primes in the 8th-order Fibonacci number sequence, A079262.

Original entry on oeis.org

9, 17, 25, 125, 350, 1322, 108935, 199528

Offset: 1

Robert Price, Jan 09 2015

a(9) > 2*10^5.

Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4

Cf. A001590, A001631, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523, A214825, A235862, A000288, A000322, A000383, A249413, A060455, A079262.

a={0,0,0,0,0,0,0,1}; step=8; lst={}; For[n=step,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,n]]; a=RotateLeft[a]; a[[step]]=sum]; lst
Flatten[Position[LinearRecurrence[{1,1,1,1,1,1,1,1},{0,0,0,0,0,0,0,1},200000],?PrimeQ]]-1 (* The program takes a long time to run *) (* _Harvey P. Dale, Apr 26 2018 *)

lista(nn) = {gf = x^7/(1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8); for (n=0, nn, if (isprime(polcoeff(gf+O(x^(n+1)), n)), print1(n, ", ")););} \\ Michel Marcus, Jan 12 2015

A163551 13th-order Fibonacci numbers: a(n) = a(n-1) + ... + a(n-13) with a(1)=...=a(13)=1.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 25, 49, 97, 193, 385, 769, 1537, 3073, 6145, 12289, 24577, 49153, 98305, 196597, 393169, 786289, 1572481, 3144769, 6289153, 12577537, 25153537, 50304001, 100601857, 201191425, 402358273, 804667393

Offset: 1

Jainit Purohit (mjainit(AT)gmail.com), Jul 30 2009

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Kai Wang, Identities for generalized enneanacci numbers, Generalized Fibonacci Sequences (2020).
Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1,1,1,1,1,1,1,1,1).

Cf. A000045 (Fibonacci numbers), A000213 (tribonacci), A000288 (tetranacci), A000322 (pentanacci), A000383 (hexanacci), A060455 (heptanacci), A123526 (octanacci), A127193 (nonanacci), A127194 (decanacci), A127624 (undecanacci), A207539 (dodecanacci).

With[{c=Table[1,{13}]},LinearRecurrence[c,c,40]] (* Harvey P. Dale, Aug 09 2013 *)

x='x+O('x^50); Vec((1-x^2 -2*x^3-3*x^4 -4*x^5-5*x^6 -6*x^7-7*x^8 -8*x^9 -9*x^10 -10*x^11 -11*x^12) / (1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10-x^11-x^12-x^13)) \\ G. C. Greubel, Jul 28 2017

a(n) = a(n-1)+a(n-2)+...+a(n-13) for n > 12, a(0)=a(1)=...=a(12)=1.

G.f.: (-1)*(-1+x^2+2*x^3+3*x^4+4*x^5+5*x^6+6*x^7+7*x^8+8*x^9+9*x^10 +10*x^11 +11*x^12) / (1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10-x^11-x^12-x^13). - Michael Burkhart, Feb 18 2012

Values adapted to the definition by R. J. Mathar, Aug 01 2009

A253333 Primes in the 7th-order Fibonacci numbers A060455.

Original entry on oeis.org

7, 13, 97, 193, 769, 1531, 3049, 6073, 12097, 24097, 95617, 379399, 2998753, 187339729, 373174033, 2949551617, 184265983633, 731152932481, 88025699967469825543, 175344042716296888429, 4979552865927484193343796114081304399449

Offset: 1

Robert Price, Dec 30 2014

nonn

a(22) is too large to display here. It has 53 digits and is the 180th term in A060455.

Robert G. Wilson v, Table of n, a(n) for n = 1..34

Cf. A001590, A001631, A100683, A231574, A231575, A232543, A214899, A020992, A233554, A214727, A234696, A141523, A235862, A214825, A235873, A001630, A241660, A247027, A000288, A247561, A000322, A248920, A000383, A247192, A060455, A253318.

a={1,1,1,1,1,1,1}; step=7; lst={}; For[n=step,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,sum]]; a=RotateLeft[a]; a[[7]]=sum]; lst
With[{c=PadRight[{},7,1]},Select[LinearRecurrence[c,c,150],PrimeQ]] (* Harvey P. Dale, May 08 2015 *)

lista(nn) = {gf = ( -1+x^2+2*x^3+3*x^4+4*x^5+5*x^6 ) / ( -1+x+x^2+x^3+x^4+x^5+x^6+x^7 ); for (n=0, nn, if (isprime(p=polcoeff(gf+O(x^(n+1)), n)), print1(p, ", ")););} \\ Michel Marcus, Jan 11 2015

A254412 Indices of primes in the 8th-order Fibonacci number sequence, A123526.

Original entry on oeis.org

11, 13, 15, 24, 30, 33, 57, 104, 121, 132, 149, 158, 178, 220, 295, 389, 1070, 1101, 1373, 1761, 1778, 2333, 2731, 4541, 5189, 5237, 5738, 8025, 8787, 10561, 11783, 13435, 14638, 15337, 20985, 21722, 24770, 31009, 57367, 65877, 129773, 134630, 167020

Offset: 1

Robert Price, Jan 30 2015

a(44) > 2*10^5.

Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4

Cf. A001590, A001631, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523, A214825, A235862, A000288, A000322, A000383, A249413, A060455, A079262, A123526, A254413.

a={1,1,1,1,1,1,1,1}; step=8; lst={}; For[n=step+1,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,n]]; a=RotateLeft[a]; a[[step]]=sum]; lst

A254413 Primes in the 8th-order Fibonacci numbers A123526.

Original entry on oeis.org

29, 113, 449, 226241, 14307889, 113783041, 1820091580429249, 233322881089059894782836851617, 29566627412209231076314948970028097, 59243719929958343565697204780596496129, 7507351981539044730893385057192143660843521

Offset: 1

Robert Price, Jan 30 2015

nonn

a(12) is too large to display here. It has 46 digits and is the 158th term in A123526.

Cf. A001590, A001631, A100683, A231574, A231575, A232543, A214899, A020992, A233554, A214727, A234696, A141523, A235862, A214825, A235873, A001630, A241660, A247027, A000288, A247561, A000322, A248920, A000383, A247192, A060455, A253318, A079262, A253705, A123526, A254412.

a={1,1,1,1,1,1,1,1}; step=8; lst={}; For[n=step+1,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,sum]]; a=RotateLeft[a]; a[[step]]=sum]; lst
Select[With[{lr=PadRight[{},8,1]},LinearRecurrence[lr,lr,200]],PrimeQ] (* Harvey P. Dale, Dec 03 2022 *)

A105527 Index when n-nacci (tribonacci etc.) passes Fibonacci numbers.

Original entry on oeis.org

3, 4, 6, 9, 11, 14, 16, 19, 22, 25, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 67, 70, 73, 76, 79, 82, 85, 88, 91, 95, 98, 101, 104, 107, 110, 113, 117, 120, 123, 126, 129, 132, 136, 139, 142, 145, 148, 151, 155, 158, 161, 164, 167, 171, 174, 177, 180, 183, 186

Offset: 3

Ferenc Adorjan (fadorjan(AT)freemail.hu), Apr 11 2005

The n-nacci sequences are considered as defined in A000213, A000288, A000322, A000383 for n=3,4,5,6, respectively.

			a(3)=3 because tribonacci(3)=3 while fibonacci(3)=2;
a(6)=9 because hexanacci(9)=41 while fibonacci(9)=34.

Cf. A105528, A000045, A000213, A000288, A000322, A000383.

{n_bonacci(n,v)= local(x,l);l=matsize(v)[2]; x=0;for(i=l-n+1,l,x+=v[i]);return(x)} {nbg(k)= local(q=[],l,v,m); for(n=3,k,v=[];for(i=1,n,v=concat(v,1));m=n; while((x=n_bonacci(n,v))<=fibonacci(m),v=concat(v,x);m+=1);q=concat(q,m)); return(q) }

A105528 First differences of A105527.

Original entry on oeis.org

1, 2, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3

Offset: 0

Ferenc Adorjan (fadorjan(AT)freemail.hu), Apr 11 2005

Note that if n>9, a(n) is seemingly either 3 or 4. Checked up to index 200.

Cf. A105527, A000045, A000213, A000288, A000322, A000383.

{n_bonacci(n,v)= local(x,l);l=matsize(v)[2]; x=0;for(i=l-n+1,l,x+=v[i]);return(x)} {nbg(k)= local(q=[],l,v,m); for(n=3,k,v=[];for(i=1,n,v=concat(v,1));m=n; while((x=n_bonacci(n,v))<=fibonacci(m),v=concat(v,x);m+=1);q=concat(q,m)); return(q) } z=nbg(100);d=[];for(i=2,98,d=concat(d,z[i]-z[i-1]))

cp's OEIS Frontend

A214830 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 8.

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A253318 Indices of primes in the 7th-order Fibonacci number sequence, A060455.

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A061451 Array T(n,k) of k-th order Fibonacci numbers read by antidiagonals in up-direction.

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A253705 Indices of primes in the 8th-order Fibonacci number sequence, A079262.

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A163551 13th-order Fibonacci numbers: a(n) = a(n-1) + ... + a(n-13) with a(1)=...=a(13)=1.

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A253333 Primes in the 7th-order Fibonacci numbers A060455.

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A254412 Indices of primes in the 8th-order Fibonacci number sequence, A123526.

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A254413 Primes in the 8th-order Fibonacci numbers A123526.

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