A079398 -id:A079398 - cp's OEIS frontend

A103376 a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = a(7) = a(8) = a(9) = 1 and for n>9: a(n) = a(n-8) + a(n-9).

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 5, 7, 8, 8, 8, 8, 8, 8, 9, 12, 15, 16, 16, 16, 16, 16, 17, 21, 27, 31, 32, 32, 32, 32, 33, 38, 48, 58, 63, 64, 64, 64, 65, 71, 86, 106, 121, 127, 128, 128, 129, 136, 157, 192, 227, 248, 255, 256, 257, 265, 293

Offset: 1

Jonathan Vos Post, Feb 05 2005

k=8 case of the family of sequences whose k=1 case is the Fibonacci sequence A000045, k=2 case is the Padovan sequence A000931 (offset so as to begin 1,1,1), k=3 case is A079398 (offset so as to begin 1,1,1,1), k=4 case is A103372, k=5 case is A103373, k=6 case is A103374 and k=7 case is A103375.
The general case for integer k>1 is defined: a(1) = a(2) = ... = a(k+1) and for n>(k+1) a(n) = a(n-k) + a(n-[k+1]).
For this k=8 case, the ratio of successive terms a(n)/a(n-1) approaches the unique positive root of the characteristic polynomial: x^9 - x - 1 = 0. This is the real constant (to 50 digits accuracy): 1.0850702454914508283368958640973142340506536310308 = A230162. Note that x = (1 + x)^(1/9) = (1 + (1 + (1 + ...)^(1/9))^(1/9))^(1/9).
The sequence of prime values in this k=8 case is A103386; The sequence of semiprime values in this k=8 case is A103396.

			a(93) = 1200 because a(93) = a(93-8) + a(93-9) = a(85) + a(84) = 642 + 558.

Zanten, A. J. van, "The golden ratio in the arts of painting, building and mathematics", Nieuw Archief voor Wiskunde, 4 (17) (1999) 229-245.

J.-P. Allouche and T. Johnson, Narayana's cows and delayed morphisms, in G. Assayag, M. Chemillier, and C. Eloy, Troisièmes Journées d'Informatique Musicale, JIM '96, Île de Tatihou, France, 1996, pp. 2-7. [The hal link does not always work. - _N. J. A. Sloane_, Feb 19 2025]
J.-P. Allouche and T. Johnson, Narayana's cows and delayed morphisms, in G. Assayag, M. Chemillier, and C. Eloy, Troisièmes Journées d'Informatique Musicale, JIM '96, Île de Tatihou, France, 1996, pp. 2-7. [Local copy with annotations and a correction from _N. J. A. Sloane_, Feb 19 2025]
Richard Padovan, Dom Hans van der Laan and the Plastic Number.
E. S. Selmer, On the irreducibility of certain trinomials, Math. Scand., 4 (1956) 287-302.
J. Shallit, A generalization of automatic sequences, Theoretical Computer Science, 61 (1988), 1-16.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1,1).

Cf. A000045, A000931, A079398, A103372-A103375, A103377-A103380, A103386, A103396.

k = 8; Do[a[n] = 1, {n, k + 1}]; a[n_] := a[n] = a[n - k] + a[n - k - 1]; Array[a, 76]
LinearRecurrence[{0,0,0,0,0,0,0,1,1},{1,1,1,1,1,1,1,1,1},80] (* Harvey P. Dale, May 07 2015 *)

a(n)=([0,1,0,0,0,0,0,0,0; 0,0,1,0,0,0,0,0,0; 0,0,0,1,0,0,0,0,0; 0,0,0,0,1,0,0,0,0; 0,0,0,0,0,1,0,0,0; 0,0,0,0,0,0,1,0,0; 0,0,0,0,0,0,0,1,0; 0,0,0,0,0,0,0,0,1; 1,1,0,0,0,0,0,0,0]^(n-1)*[1;1;1;1;1;1;1;1;1])[1,1] \\ Charles R Greathouse IV, Oct 03 2016

G.f.: x*(1+x)*(1+x^2)*(1+x^4)/(1-x^8-x^9). - R. J. Mathar, Dec 14 2009

a(1)=1, a(2)=1, a(3)=1, a(4)=1, a(5)=1, a(6)=1, a(7)=1, a(8)=1, a(9)=1, a(n)=a(n-8)+a(n-9). - Harvey P. Dale, May 07 2015

Edited by Ray Chandler, Feb 10 2005

A103397 Semiprimes in A103377.

Original entry on oeis.org

4, 9, 15, 21, 33, 38, 58, 65, 86, 106, 121, 129, 265, 511, 8114, 8193, 16307, 16853, 17855, 19857, 31298, 68037, 104739, 124205, 131209, 134149, 140457, 152849, 252914, 259918, 265358, 274606, 417527, 2498871, 5291863, 8424051, 8743821

Offset: 1

Jonathan Vos Post, Feb 15 2005

			2071468241 is an element of A103377 and 2071468241= 17 * 121851073 which shows that it is a semiprime.

Cf. A001358, A000931, A079398, A103372-103381, A103377, A103397.

SemiprimeQ[n_]:=Plus@@FactorInteger[n][[All, 2]]?2; Clear[a]; k=9; Do[a[n]=1, {n, k+1}]; a[n_]:=a[n]=a[n-k]+a[n-k-1]; A103377=Array[a, 100] A103387=Union[Select[Array[a, 1000], PrimeQ]] A103397=Union[Select[Array[a, 300], SemiprimeQ]] N[Solve[x^10 - x - 1 == 0, x], 111][[2]]

Intersection of A103377 with A001358.

A103633 Triangle read by rows: triangle of repeated stepped binomial coefficients.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 1, 4, 6, 4, 1, 0, 0, 0, 0, 0, 1, 4, 6, 4, 1, 0, 0, 0, 0, 0, 1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0, 0, 1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0, 0, 1, 6, 15, 20, 15, 6, 1, 0, 0, 0, 0, 0, 0, 0, 1, 6, 15

Offset: 0

Paul Barry, Feb 11 2005

Row sums are Sum_{k=0..n} binomial(floor(n/2),n-k) = (1,1,2,2,4,4,...). Diagonal sums have g.f. (1+x^2)/(1-x^3-x^4) (see A079398). Matrix inverse of the signed triangle (-1)^(n-k)T(n,k) is A103631. Matrix inverse of T(n,k) is the alternating signed version of A103631.

Triangle T(n,k), 0 <= k <= n, read by rows, given by [0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ....] DELTA [1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938. - Philippe Deléham, Oct 08 2005

			Triangle begins:
  1;
  0,  1;
  0,  1,  1;
  0,  0,  1,  1;
  0,  0,  1,  2,  1;
  0,  0,  0,  1,  2,  1;
  0,  0,  0,  1,  3,  3,  1;
  0,  0,  0,  0,  1,  3,  3,  1;
  0,  0,  0,  0,  1,  4,  6,  4,  1;
  0,  0,  0,  0,  0,  1,  4,  6,  4,  1;
  0,  0,  0,  0,  0,  1,  5, 10, 10,  5,  1;
  0,  0,  0,  0,  0,  0,  1,  5, 10, 10,  5,  1;
  0,  0,  0,  0,  0,  0,  1,  6, 15, 20, 15,  6,  1; ...

Number triangle T(n, k) = binomial(floor(n/2), n-k).
Sum_{n>=0} T(n, k) = A000045(k+2) = Fibonacci(k+2). - Philippe Deléham, Oct 08 2005
Sum_{k=0..n} T(n,k) = 2^floor(n/2) = A016116(n). - Philippe Deléham, Dec 03 2006
G.f.: (1+x*y)/(1-x^2*y-x^2*y^2). - Philippe Deléham, Nov 10 2013
T(n,k) = T(n-2,k-1) + T(n-2,k-2) for n > 2, T(0,0) = T(,1) = T(2,1) = T(2,2) = 1, T(1,0) = T(2,0) = 0, T(n,k) = 0 if k > n or if k < 0. - Philippe Deléham, Nov 10 2013

A376649 a(n) = Sum_{k=0..floor(n/3)} binomial(floor(k/3),n-3*k).

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 3, 3, 2, 3, 3, 2, 3, 3, 2, 4, 6, 5, 5, 6, 5, 5, 6, 5, 6, 10, 11, 10, 11, 11, 10, 11, 11, 11, 16, 21, 21, 21, 22, 21, 21, 22, 22, 27, 37, 42, 42, 43, 43, 42, 43, 44, 49, 64, 79, 84, 85, 86, 85, 85, 87, 93, 113, 143

Offset: 0

Seiichi Manyama, Oct 01 2024

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

Cf. A079398, A376650.

Cf. A017877.

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

my(N=90, x='x+O('x^N)); Vec((1+x^3+x^6)/(1-x^9-x^10))

G.f.: (1-x^9)/((1-x^3) * (1-x^9-x^10)) = (1+x^3+x^6)/(1-x^9-x^10).
a(n) = a(n-9) + a(n-10).
a(n) = A017877(n) + A017877(n-3) + A017877(n-6).

A137166 Sequence equals its 4th differences shifted by one index.

Original entry on oeis.org

1, 3, 7, 15, 32, 70, 156, 349, 778, 1728, 3833, 8505, 18884, 41943, 93160, 206897, 459459, 1020311, 2265815, 5031792, 11174374, 24815508, 55108933, 122382762, 271780616, 603555049, 1340341377, 2976555532, 6610168495, 14679492624

Offset: 0

Vladimir Joseph Stephan Orlovsky, Apr 03 2008

Binomial transform yields A079398 without the initial (0,1,1,1). - R. J. Mathar, Apr 09 2008

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,5,-1).

Cf. A079398.

[n le 4 select 2^n-1 else 4*Self(n-1)-6*Self(n-2)+5*Self(n-3)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jun 15 2013

s = ""; a = 0; b = 1; c = 1; d = 1; For[i = 0, i < 23, a = a + b; s = s <> ToString[a] <> ","; b = b + c; c = c + d; d = d + a; i++ ]; Print[s]
LinearRecurrence[{4, -6, 5, -1}, {1, 3, 7, 15}, 40] (* Vincenzo Librandi, Jun 15 2013 *)

a(n)=([0,1,0,0; 0,0,1,0; 0,0,0,1; -1,5,-6,4]^n*[1;3;7;15])[1,1] \\ Charles R Greathouse IV, Oct 03 2016

a(n) = 4*a(n-1)-6*a(n-2)+5*a(n-3)-a(n-4). - R. J. Mathar, Apr 09 2008

G.f.: (x^2 - x + 1) / (x^4 - 5*x^3 + 6*x^2 - 4*x + 1). - Alexander R. Povolotsky, Apr 08 2008

Edited by R. J. Mathar, Apr 09 2008

Edited by Bruno Berselli, Apr 07 2011

A242763 a(n) = 1 for n <= 7; a(n) = a(n-5) + a(n-7) for n>7.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 7, 7, 8, 9, 9, 12, 12, 15, 16, 17, 21, 21, 27, 28, 32, 37, 38, 48, 49, 59, 65, 70, 85, 87, 107, 114, 129, 150, 157, 192, 201, 236, 264, 286, 342, 358, 428, 465, 522, 606, 644, 770, 823, 950, 1071, 1166, 1376

Offset: 1

Vicente Jesús Maniega Granado, Oct 03 2016

Generalized Fibonacci growth sequence using i = 2 as maturity period, j = 5 as conception period, and k = 2 as growth factor.

Maturity period is the number of periods that a Fibonacci tree node needs for being able to start developing branches. Conception period is the number of periods in a Fibonacci tree node needed to develop new branches since its maturity. Growth factor is the number of additional branches developed by a Fibonacci tree node, plus 1, and equals the base of the exponential series related to the given tree if maturity factor would be zero. Standard Fibonacci would use 1 as maturity period, 1 as conception period, and 2 as growth factor as the series becomes equal to 2^n with a maturity period of 0. Related to Lucas sequences.

			For n = 13 the a(13) = a(8) + a(6) = 2 + 1 = 3.

Colin Barker, Table of n, a(n) for n = 1..1000
Julia Collins, Fibonacci Tree
Fractal Foundation, Fibonacci Fractals
D. H. Lehmer, An extended theory of Lucas' functions, Annals of Mathematics, Second Series, Vol. 31, No. 3 (Jul., 1930), pp. 419-448.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1,0,1).

Cf. A000079 (i = 0, j = 1, k = 2), A000244 (i = 0, j = 1, k = 3), A000302 (i = 0, j = 1, k = 4), A000351 (i = 0, j = 1, k = 5), A000400 (i = 0, j = 1, k = 6), A000420 (i = 0, j = 1, k = 7), A001018 (i = 0, j = 1, k = 8), A001019 (i = 0, j = 1, k = 9), A011557 (i = 0, j = 1, k = 10), A001020 (i = 0, j = 1, k = 11), A001021 (i = 0, j = 1, k = 12), A016116 (i = 0, j = 2, k = 2), A108411 (i = 0, j = 2, k = 3), A213173 (i = 0, j = 2, k = 4), A074872 (i = 0, j = 2, k = 5), A173862 (i = 0, j = 3, k = 2), A127975 (i = 0, j = 3, k = 3), A200675 (i = 0, j = 4, k = 2), A111575 (i = 0, j = 4, k = 3), A000045 (i = 1, j = 1, k = 2), A001045 (i = 1, j = 1, k = 3), A006130 (i = 1, j = 1, k = 4), A006131 (i = 1, j = 1, k = 5), A015440 (i = 1, j = 1, k = 6), A015441 (i = 1, j = 1, k = 7), A015442 (i = 1, j = 1, k = 8), A015443 (i = 1, j = 1, k = 9), A015445 (i = 1, j = 1, k = 10), A015446 (i = 1, j = 1, k = 11), A015447 (i = 1, j = 1, k = 12), A000931 (i = 1, j = 2, k = 2), A159284 (i = 1, j = 2, k = 3), A238389 (i = 1, j = 2, k = 4), A097041 (i = 1, j = 2, k = 10), A079398 (i = 1, j = 3, k = 2), A103372 (i = 1, j = 4, k = 2), A103373 (i = 1, j = 5, k = 2), A103374 (i = 1, j = 6, k = 2), A000930 (i = 2, j = 1, k = 2), A077949 (i = 2, j = 1, k = 3), A084386 (i = 2, j = 1, k = 4), A089977 (i = 2, j = 1, k = 5), A178205 (i = 2, j = 1, k = 11), A103609 (i = 2, j = 2, k = 2), A077953 (i = 2, j = 2, k = 3), A226503 (i = 2, j = 3, k = 2), A122521 (i = 2, j = 6, k = 2), A003269 (i = 3, j = 1, k = 2), A052942 (i = 3, j = 1, k = 3), A005686 (i = 3, j = 2, k = 2), A237714 (i = 3, j = 2, k = 3), A238391 (i = 3, j = 2, k = 4), A247049 (i = 3, j = 3, k = 2), A077886 (i = 3, j = 3, k = 3), A003520 (i = 4, j = 1, k = 2), A108104 (i = 4, j = 2, k = 2), A005708 (i = 5, j = 1, k = 2), A237716 (i = 5, j = 2, k = 3), A005709 (i = 6, j = 1, k = 2), A122522 (i = 6, j = 2, k = 2), A005710 (i = 7, j = 1, k = 2), A237718 (i = 7, j = 2, k = 3), A017903 (i = 8, j = 1, k = 2).

[n le 7 select 1 else Self(n-5)+Self(n-7): n in [1..70]]; // Vincenzo Librandi, Nov 30 2016

LinearRecurrence[{0, 0, 0, 0, 1, 0, 1}, {1, 1, 1, 1, 1, 1, 1}, 70] (*  or *)
CoefficientList[ Series[(1+x+x^2+x^3+x^4)/(1-x^5-x^7), {x, 0, 70}], x] (* Robert G. Wilson v, Nov 25 2016 *)
nxt[{a_,b_,c_,d_,e_,f_,g_}]:={b,c,d,e,f,g,a+c}; NestList[nxt,{1,1,1,1,1,1,1},70][[;;,1]] (* Harvey P. Dale, Oct 22 2024 *)

Vec(x*(1+x+x^2+x^3+x^4)/((1-x+x^2)*(1+x-x^3-x^4-x^5)) + O(x^100)) \\ Colin Barker, Oct 27 2016

@CachedFunction # a = A242763
def a(n): return 1 if n<8 else a(n-5) +a(n-7)
[a(n) for n in range(1,76)] # G. C. Greubel, Oct 23 2024

Generic a(n) = 1 for n <= i+j; a(n) = a(n-j) + (k-1)*a(n-(i+j)) for n>i+j where i = maturity period, j = conception period, k = growth factor.
G.f.: x*(1+x+x^2+x^3+x^4) / ((1-x+x^2)*(1+x-x^3-x^4-x^5)). - Colin Barker, Oct 09 2016
Generic g.f.: x*(Sum_{l=0..j-1} x^l) / (1-x^j-(k-1)*x^(i+j)), with i > 0, j > 0 and k > 1.

A307677 a(0) = a(1) = a(2) = a(3) = 1; thereafter a(n) = a(n-1) + a(n-2) + a(n-4).

Original entry on oeis.org

1, 1, 1, 1, 3, 5, 9, 15, 27, 47, 83, 145, 255, 447, 785, 1377, 2417, 4241, 7443, 13061, 22921, 40223, 70587, 123871, 217379, 381473, 669439, 1174783, 2061601, 3617857, 6348897, 11141537, 19552035, 34311429, 60212361, 105665327, 185429723, 325406479, 571048563, 1002120369

Offset: 0

Joseph Damico, Apr 21 2019

A079398, A103609, A003269, A306276, A126116, and A000288 are the other six sequences which have characteristic equations of the form x^4 = ax^3 + bx^2 + cx + 1 in which a, b, and c are equal to either 0 or 1 -- but not all three of them are equal to zero. (Each of those sequences begins with 1,1,1,1.)
A005251 has the same characteristic equation, and each successive term is determined by the same operation, namely, a(n) = a(n-1) + a(n-2) + a(n-4). However, it has different starting values: (0,1,1,1) instead of (1,1,1,1).
The characteristic equation of this sequence is x^4 = x^3 + x^2 + 1. Lim_{n->infinity} a(n+1)/a(n) = 1.754877666...

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

Cf. A000288, A003269, A005251, A005314, A079398, A103609, A126116, A306276.

[n le 4 select 1 else Self(n-1) +Self(n-2) +Self(n-4): n in [1..51]]; // G. C. Greubel, Oct 23 2024

LinearRecurrence[{1,1,0,1}, {1,1,1,1}, 51] (* G. C. Greubel, Oct 23 2024 *)

Vec((1 - x^2 - x^3) / ((1 + x)*(1 - 2*x + x^2 - x^3)) + O(x^40)) \\ Colin Barker, Apr 25 2020

@CachedFunction # a = A307677
def a(n): return 1 if n<4 else a(n-1) +a(n-2) +a(n-3)
[a(n) for n in range(51)] # G. C. Greubel, Oct 23 2024

From Colin Barker, Apr 25 2020: (Start)
G.f.: (1 - x^2 - x^3) / ((1 + x)*(1 - 2*x + x^2 - x^3)).
a(n) = a(n-1) + a(n-2) + a(n-4) for n>3. (End)
a(n) = (1/5)*((-1)^n + 2*(2*A005314(n+1) - A005314(n) - 2*A005314(n-1))). - G. C. Greubel, Oct 23 2024

A376650 a(n) = Sum_{k=0..floor(n/4)} binomial(floor(k/3),n-4*k).

Original entry on oeis.org

1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 5, 10, 10, 6, 6, 10, 10, 6, 6, 10, 10, 6, 7, 15, 20, 16, 12, 16, 20, 16, 12, 16, 20, 16, 13, 22, 35, 36

Offset: 0

Seiichi Manyama, Oct 01 2024

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

Cf. A079398, A376649.

a(n) = sum(k=0, n\4, binomial(k\3, n-4*k));

my(N=90, x='x+O('x^N)); Vec((1+x^4+x^8)/(1-x^12-x^13))

G.f.: (1-x^12)/((1-x^4) * (1-x^12-x^13)) = (1+x^4+x^8)/(1-x^12-x^13).

a(n) = a(n-12) + a(n-13).

A385106 a(n) = 3a(n-1) - 3a(n-2) + a(n-3) + a(n-4) with a(1) = 1, a(2) = 2, a(3) = 4, and a(4) = 7.

Original entry on oeis.org

1, 2, 4, 7, 12, 21, 38, 70, 129, 236, 429, 778, 1412, 2567, 4672, 8505, 15478, 28158, 51217, 93160, 169465, 308290, 560852, 1020311, 1856132, 3376605, 6142582, 11174374, 20328113, 36980404, 67273829, 122382762, 222635316, 405011895, 736786328, 1340341377, 2438312358, 4435711166

Offset: 1

Hung Viet Chu, Jun 18 2025

a(n) the number of subsets of {3, 6, 9, 12, ..., 3*n} that are Schreier and contain 3*n.

Hung Viet Chu and Zachary Louis Vasseur, Schreier sets of multiples of an integer, linear recurrence, and Pascal triangle, arXiv:2506.14312 [math.CO], 2025. See Table 1 p. 2.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1,1)

Cf. A079398, A385107.

LinearRecurrence[{3,-3,1,1},{1, 2, 4, 7},38 ] (* or *) Rest[CoefficientList[Series[x*(1 - x + x^2)/(1 - 3*x + 3*x^2 - x^3 - x^4),{x,0,38}],x]] (* or *) a[1]=1;a[n_]:=2 + Sum[Binomial[n-i-1,j],{i,n-2} ,{j,0,3i-2} ];Array[a,38] (* James C. McMahon, Jun 24 2025 *)

a(n) = 2 + Sum_{i=1..n-2} Sum_{j=0..3i-2} binomial(n-i-1,j), for n > 1.
a(n) = A079398(3*n).
G.f.: x*(1 - x + x^2)/(1 - 3*x + 3*x^2 - x^3 - x^4).

A321025 a(n) = sum of a(n-4) and a(n-5), with the lowest possible initial values that will generate a sequence where a(n) is always > a(n-1): 4, 5, 6, 7 and 8.

Original entry on oeis.org

4, 5, 6, 7, 8, 9, 11, 13, 15, 17, 20, 24, 28, 32, 37, 44, 52, 60, 69, 81, 96, 112, 129, 150, 177, 208, 241, 279, 327, 385, 449, 520, 606, 712, 834, 969, 1126, 1318, 1546, 1803, 2095, 2444, 2864, 3349, 3898, 4539, 5308, 6213, 7247, 8437, 9847, 11521, 13460, 15684

Offset: 1

Mathew Munro, Oct 30 2018

A sum of prior terms in the sequence, like the Fibonacci and Padovan sequences.

			a(6) = a(6-4) + a(6-5) = a(2) + a(1) = 5 + 4 = 9.

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

Cf. A000045, A000931, A079398, A164317, A103372, A103373

Rest@ CoefficientList[Series[x (4 + 5 x + 6 x^2 + 7 x^3 + 4 x^4)/(1 - x^4 - x^5), {x, 0, 54}], x] (* Michael De Vlieger, Oct 31 2018 *)

a(n) = if(n<=5, n+3, a(n-4) + a(n-5)); \\ Michel Marcus, Oct 31 2018

Vec((4 + 5*x + 6*x^2 + 7*x^3 + 4*x^4)/(1 - x^4 - x^5) + O(x^50)) \\ Andrew Howroyd, Oct 31 2018

a(n) = a(n-4) + a(n-5) with a(1) = 4, a(2) = 5, a(3) = 6, a(4) = 7 and a(5) = 8.

G.f.: x*(4 + 5*x + 6*x^2 + 7*x^3 + 4*x^4)/(1 - x^4 - x^5). - Andrew Howroyd, Oct 31 2018

a(19), a(20) corrected by Georg Fischer, May 24 2019

cp's OEIS Frontend

A103376 a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = a(7) = a(8) = a(9) = 1 and for n>9: a(n) = a(n-8) + a(n-9).

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A103397 Semiprimes in A103377.

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A103633 Triangle read by rows: triangle of repeated stepped binomial coefficients.

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A376649 a(n) = Sum_{k=0..floor(n/3)} binomial(floor(k/3),n-3*k).

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A137166 Sequence equals its 4th differences shifted by one index.

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A242763 a(n) = 1 for n <= 7; a(n) = a(n-5) + a(n-7) for n>7.

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A307677 a(0) = a(1) = a(2) = a(3) = 1; thereafter a(n) = a(n-1) + a(n-2) + a(n-4).

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A385106 a(n) = 3a(n-1) - 3a(n-2) + a(n-3) + a(n-4) with a(1) = 1, a(2) = 2, a(3) = 4, and a(4) = 7.