A103379 -id:A103379 - cp's OEIS frontend

A103389 Primes in A103379.

2, 3, 5, 7, 17, 31, 71, 127, 157, 227, 257, 293, 349, 419, 503, 8179, 65657, 68053, 72421, 80429, 258949, 493109, 16399511, 33609887, 34225183, 1387603957, 5575987679, 15932884421, 35689079297, 693128029907, 957136790429, 1129233918343, 10363690074667, 41632551979939, 10815125582078291

Offset: 1

Jonathan Vos Post, Feb 15 2005

			A103379(20) = 3, which is prime, hence 3 is in this sequence.

Cf. A103379, A103399.

A103379 := proc(n) option remember ; if n <= 12 then 1; else procname(n-11)+procname(n-12) ; fi; end: isA103379 := proc(n) option remember ; local i ; for i from 1 do if A103379(i) = n then RETURN(true) ; elif A103379(i) > n then RETURN(false) ; fi; od: end: A103389 := proc(n) option remember ; local a; if n = 1 then 2; else for a from procname(n-1)+1 do if isprime(a) then if isA103379(a) then RETURN(a) ; fi; fi; od: fi; end: for n from 1 to 37 do printf("%d, ",A103389(n)) ; od: # R. J. Mathar, Aug 30 2008

Clear[a]; k11; Do[a[n]=1, {n, k+1}]; a[n_]:=a[n]=a[n-k]+a[n-k-1]; A103389=Union[Select[Array[a, 1000], PrimeQ]] N[Solve[x^12 - x - 1 == 0, x], 111][[2]] (* Program, edit and extension by Ray Chandler and Robert G. Wilson v, irrelevant code deleted by M. F. Hasler, Sep 19 2015 *)
Select[LinearRecurrence[{0,0,0,0,0,0,0,0,0,0,1,1},{1,1,1,1,1,1,1,1,1,1,1,1},700],PrimeQ]//Union (* Harvey P. Dale, Apr 22 2016 *)

{a=vector(m=12,n,1);L=0;for(n=m,10^5,isprime(a[i=n%m+1]+=a[(n+1)%m+1])&&LM. F. Hasler, Sep 19 2015

Intersection of A103379 and A000040.

Corrected from a(16) on by R. J. Mathar, Aug 30 2008

Edited and more terms added by M. F. Hasler, Sep 19 2015

A103399 Semiprimes in A103379.

Original entry on oeis.org

4, 9, 15, 21, 33, 38, 58, 65, 86, 106, 121, 129, 265, 511, 2047, 2049, 4097, 4109, 17855, 19857, 32663, 34709, 104739, 130393, 131889, 140474, 220918, 262978, 266174, 274759, 540933, 568083, 1312526, 1665242, 1833203, 2179101, 2295571

Offset: 1

Jonathan Vos Post, Feb 15 2005

nonn

			A103379(21) = 4 = 2 * 2, which is semiprime, hence 4 is in this sequence.

Cf. A001358, A103379, A103389.

isA103379 := proc(n)
    option remember ;
    local i ;
    for i from 1 do
        if A103379(i) = n then
            return true ;
        elif A103379(i) > n then
            return false ;
        fi;
    od:
end proc:
A103399 := proc(n)
    option remember ;
    local a, i ;
    if n = 1 then
        4;
    else
        for a from procname(n-1)+1 do
            if numtheory[bigomega](a) = 2 then
                if isA103379(a) then
                    return a ;
                fi;
            fi;
        end do:
    end if;
end proc:
for n from 1 do
    printf("%d,\n",A103399(n)) ;
end do: # R. J. Mathar, Aug 30 2008

SemiprimeQ[n_]:=Plus@@FactorInteger[n][[All, 2]]?2; Clear[a]; k11; Do[a[n]=1, {n, k+1}]; a[n_]:=a[n]=a[n-k]+a[n-k-1]; A103379=Array[a, 100] A103389=Union[Select[Array[a, 1000], PrimeQ]] A103399=Union[Select[Array[a, 300], SemiprimeQ]] N[Solve[x^12 - x - 1 == 0, x], 111][[2]] (* Program, edit and extension by Ray Chandler and Robert G. Wilson v *)

Intersection of A103379 and A001358.

Corrected from a(15) on by R. J. Mathar, Aug 30 2008

A103380 a(n) = a(n-12) + a(n-13).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 12, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 21, 27, 31, 32, 32, 32, 32, 32, 32, 32, 32, 33, 38, 48, 58, 63, 64, 64, 64, 64, 64, 64, 64, 65

Offset: 1

Jonathan Vos Post, Feb 16 2005

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

Cf. A079398, A103372-A103379, A103400.

A103380 := proc(n) option remember ; if n <= 13 then 1; else procname(n-12)+procname(n-13) ; fi; end: for n from 1 to 120 do printf("%d,",A103380(n)) ; od: # R. J. Mathar, Aug 30 2008

LinearRecurrence[{0,0,0,0,0,0,0,0,0,0,0,1,1},{1,1,1,1,1,1,1,1,1,1,1,1,1},90] (* Harvey P. Dale, Jul 16 2012 *)

For n>13: a(n) = a(n-12) + a(n-13). a(1) = a(2) = ... = a(13) = 1.

G.f.: x*(1-x^12) / ((1-x)*(1-x^12-x^13)). - Colin Barker, Mar 27 2013

Terms from a(11) on corrected by R. J. Mathar, Aug 30 2008

A103373 a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = 1 and for n>6: a(n) = a(n-5) + a(n-6).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 5, 7, 8, 8, 8, 9, 12, 15, 16, 16, 17, 21, 27, 31, 32, 33, 38, 48, 58, 63, 65, 71, 86, 106, 121, 128, 136, 157, 192, 227, 249, 264, 293, 349, 419, 476, 513, 557, 642, 768, 895, 989, 1070, 1199, 1410, 1663, 1884, 2059, 2269

Offset: 1

Jonathan Vos Post, Feb 03 2005

k=5 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) and k=4 case is A103372.
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=5 case, the ratio of successive terms a(n)/a(n-1) approaches the unique positive root of the characteristic polynomial: x^6 - x - 1 = 0. This is the real constant 1.1347241384015194926054460545064728402796672263828014859251495516682....
The sequence of prime values in this k=5 case is A103383; the sequence of semiprime values in this k=5 case is A103393.

			a(22) = 9 because a(22) = a(22-5) + a(22-6) = a(17) + a(16) = 5 + 4 = 9.

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

G. C. Greubel, Table of n, a(n) for n = 1..1000
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 (0,0,0,0,1,1).

Cf. A000045, A000931, A079398, A103383, A103393.

Cf. A103372, A103374, A103375, A103376, A103377, A103378, A103379, A103380

k = 5; Do[a[n] = 1, {n, k + 1}]; a[n_] := a[n] = a[n - k] + a[n - k - 1]; Array[a, 65]
RecurrenceTable[{a[n] == a[n - 5] + a[n - 6], a[1] == a[2] == a[3] == a[4] == a[5] == a[6] == 1}, a, {n, 65}] (* or *)
Rest@ CoefficientList[Series[-x (1 + x + x^2 + x^3 + x^4)/(-1 + x^5 + x^6), {x, 0, 65}], x] (* Michael De Vlieger, Oct 03 2016 *)
LinearRecurrence[{0,0,0,0,1,1},{1,1,1,1,1,1},70] (* Harvey P. Dale, Jul 20 2019 *)

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

x='x+O('x^50); Vec(x*(1+x+x^2+x^3+x^4)/(1-x^5-x^6 )) \\ G. C. Greubel, May 01 2017

G.f.: x*(1+x+x^2+x^3+x^4) / (1-x^5-x^6 ). - R. J. Mathar, Aug 26 2011

Edited by Ray Chandler and Robert G. Wilson v, Feb 06 2005

A103374 a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = a(7) = 1 and for n>7: a(n) = a(n-6) + a(n-7).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 5, 7, 8, 8, 8, 8, 9, 12, 15, 16, 16, 16, 17, 21, 27, 31, 32, 32, 33, 38, 48, 58, 63, 64, 65, 71, 86, 106, 121, 127, 129, 136, 157, 192, 227, 248, 256, 265, 293, 349, 419, 475, 504, 521, 558, 642, 768, 894, 979, 1025, 1079

Offset: 1

Jonathan Vos Post, Feb 03 2005

k=6 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 and k=5 case is A103373.
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=6 case, the ratio of successive terms a(n)/a(n-1) approaches the unique positive root of the characteristic polynomial: x^7 - x - 1 = 0. This is the real constant 1.1127756842787... (see A230160).
The sequence of prime values in this k=6 case is A103384; the sequence of semiprime values in this k=6 case is A103394.

			a(32) = 17 because a(32) = a(32-6) + a(32-7) = a(26) + a(25) = 9 + 8 = 17.

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

G. C. Greubel, Table of n, a(n) for n = 1..1000
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 (0,0,0,0,0,1,1).

Cf. A000045, A000931, A079398, A103384, A103394, A230160.

Cf. A103372, A103373, A103375, A103376, A103377, A103378, A103379, A103380

k = 6; Do[a[n] = 1, {n, k + 1}]; a[n_] := a[n] = a[n - k] + a[n - k - 1]; Array[a, 70]
RecurrenceTable[{a[n] == a[n - 6] + a[n - 7], a[1] == a[2] == a[3] == a[4] == a[5] == a[6] == a[7] == 1}, a, {n, 70}] (* or *)
Rest@ CoefficientList[Series[-x (1 + x) (1 + x + x^2) (x^2 - x + 1)/(-1 + x^6 + x^7), {x, 0, 70}], x] (* Michael De Vlieger, Oct 03 2016 *)
LinearRecurrence[{0,0,0,0,0,1,1},{1,1,1,1,1,1,1},80] (* Harvey P. Dale, Sep 02 2024 *)

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

x='x+O('x^50); Vec(x*(1+x)*(1+x+x^2)*(x^2-x+1)/(1-x^6-x^7)) \\ G. C. Greubel, May 01 2017

G.f.: x*(1+x)*(1+x+x^2)*(x^2-x+1) / ( 1-x^6-x^7 ). - R. J. Mathar, Aug 26 2011

Edited by Ray Chandler and Robert G. Wilson v, Feb 06 2005

A103377 a(1)=a(2)=...=a(10)=1, a(n)=a(n-9)+a(n-10).

Original entry on oeis.org

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

Offset: 1

Jonathan Vos Post, Feb 15 2005

k=9 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, k=7 case is A103375, k=8 case is A103376, k=10 case is A103378 and k=11 case is A103379. The general case for integer k>1 is defined: a(1) = a(2) = ... = a(k+1)= 1 and for n>(k+1) a(n) = a(n-k) + a(n-[k+1]). For this k=9 case, the ratio of successive terms a(n)/a(n-1) approaches the unique positive root of the characteristic polynomial: x^10 - x - 1 = 0. This is the real constant (to 50 digits accuracy): 1.0757660660868371580595995241652758206925302476392 = A230163. Note that x = (1 + x)^(1/10) = (1 + (1 + (1 + ...)^(1/10))^(1/10))^(1/10). The sequence of prime values in this k=9 case is A103387; The sequence of semiprime values in this k=9 case is A103397.

In analogy to the Fibonacci sequence, one might prefer to start this sequence with offset 0. - M. F. Hasler, Sep 19 2015

			a(83) = 257 because a(83) = a(83-9) + a(83-10). a(74) + a(73) = 129 + 128. This sequence has as elements 5, 17 and 257, which are all Fermat Primes.

A. J. van Zanten, The golden ratio in the arts of painting, building and mathematics, Nieuw Archief voor Wiskunde, vol 17 no 2 (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) 291-306
J. Shallit, A generalization of automatic sequences, Theoretical Computer Science, 61(1988)1-16.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1,1).

Cf. A000045, A000931, A079398, A103372-A103376, A103378-A103380, A103387, A103397.

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, 90] (* Charles R Greathouse IV, Jan 11 2013 *)

Vec((1+x+x^2)*(1+x^3+x^6)/(1-x^9-x^10)+O(x^99)) \\ Charles R Greathouse IV, Jan 11 2013

a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = a(7) = a(8) = a(9) = a(10) = 1 and for n>10: a(n) = a(n-9) + a(n-10).

O.g.f.: -x*(x^2+x+1)*(x^6+x^3+1)/(-1+x^9+x^10). - R. J. Mathar, May 02 2008

Edited by R. J. Mathar, May 02 2008

Edited by M. F. Hasler, Sep 19 2015

A103378 a(n) = a(n-10) + a(n-11) for n > 11, and a(n) = 1 for 1 <= n <= 11.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 12, 15, 16, 16, 16, 16, 16, 16, 16, 17, 21, 27, 31, 32, 32, 32, 32, 32, 32, 33, 38, 48, 58, 63, 64, 64, 64, 64, 64, 65, 71, 86, 106, 121, 127, 128

Offset: 1

Jonathan Vos Post, Feb 15 2005

			a(52)=17 because a(52)=a(52-10)+a(52-11) = a(42)+a(41) = 9 + 8.

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

Cf. A079398, A103372-A103377, A103379-A103380, A103388, A103398.

A103378 := proc(n) option remember; if n <= 11 then 1 ; else A103378(n-10)+A103378(n-11) ; fi ; end: seq(A103378(n),n=1..78) ; # R. J. Mathar, Nov 22 2007

k=10; Do[a[n]=1, {n, k+1}]; a[n_]:=a[n]=a[n-k]+a[n-k-1]; A103377=Array[a, 100] N[Solve[x^10 - x - 1 == 0, x], 111][[2]]
LinearRecurrence[Join[Table[0,{9}],{1,1}],Table[1,{11}],80] (* Harvey P. Dale, Aug 14 2013 *)

Vec((x^10-1)/(x-1)/(1-x^10-x^11)+O(x^80)) \\ M. F. Hasler, Sep 19 2015

G.f.: x*(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9)/(1-x^10-x^11). - R. J. Mathar, Nov 22 2007

Corrected and extended by R. J. Mathar, Nov 22 2007

Edited by M. F. Hasler, Sep 19 2015

A103400 Semiprimes in A103380.

Original entry on oeis.org

4, 9, 15, 21, 33, 38, 58, 65, 86, 106, 121, 129, 265, 511, 2047, 2049, 4097, 4109, 8193, 17855, 19857, 34709, 66233, 104739, 130953, 131209, 140474, 220918, 258931, 511673, 540951

Offset: 1

Jonathan Vos Post, Feb 16 2005

Cf. A001358, A103380.

A103380 := proc(n) option remember ; if n <= 13 then 1; else procname(n-12)+procname(n-13) ; fi; end: isA103380 := proc(n) option remember ; local i ; for i from 1 do if A103380(i) = n then RETURN(true) ; elif A103380(i) > n then RETURN(false) ; fi; od: end: A103400 := proc(n) option remember ; local a,i ; if n = 1 then 4; else for a from procname(n-1)+1 do if numtheory[bigomega](a) = 2 then if isA103380(a) then RETURN(a) ; fi; fi; od: fi; end: for n from 1 to 37 do printf("%d, ",A103400(n)) ; od: # R. J. Mathar, Aug 30 2008

SemiprimeQ[n_]:=Plus@@FactorInteger[n][[All, 2]]?2; Clear[a]; k12; Do[a[n]=1, {n, k+1}]; a[n_]:=a[n]=a[n-k]+a[n-k-1]; A103379=Array[a, 100] A103389=Union[Select[Array[a, 1000], PrimeQ]] A103399=Union[Select[Array[a, 300], SemiprimeQ]] N[Solve[x^12 - x - 1 == 0, x], 111][[2]] (* Program, edit and extension by Ray Chandler and Robert G. Wilson v *)

Intersection of A103380 and A001358.

Corrected from a(15) on by R. J. Mathar, Aug 30 2008

A152849 Triangle read by rows, A007318 rows repeated eleven times .

Original entry on oeis.org

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

Offset: 0

Philippe Deléham, Dec 14 2008

Diagonal sums : A103379 .

			Triangle begins : 1 ; 1 ; 1 ; 1 ; 1 ; 1 ; 1 ; 1 ; 1 ; 1 ; 1 ; 1,1 ; 1,1 ; 1,1 ; 1,1 ; 1,1 ; 1,1 ; 1,1 ; 1,1 ; 1,1 ; 1,1 ; 1,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,3,3,1 ; ...

Cf. A007318, A152198, A152815, A152828, A152830, A152831, A152844, A152845, A152846, A152847, A152848

Flatten[Table[#, {11}] & /@ Table[Binomial[n, k], {n, 0, 10}, {k, 0, n}]] (* G. C. Greubel, May 04 2017 *)

cp's OEIS Frontend

A103389 Primes in A103379.

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A103399 Semiprimes in A103379.

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A103380 a(n) = a(n-12) + a(n-13).

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A103373 a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = 1 and for n>6: a(n) = a(n-5) + a(n-6).

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PARI

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A103374 a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = a(7) = 1 and for n>7: a(n) = a(n-6) + a(n-7).

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PARI

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A103377 a(1)=a(2)=...=a(10)=1, a(n)=a(n-9)+a(n-10).

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A103378 a(n) = a(n-10) + a(n-11) for n > 11, and a(n) = 1 for 1 <= n <= 11.