A074089 -id:A074089 - cp's OEIS frontend

A074355 Coefficient of q^1 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=bnu(n-1)+lambda(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(1,3).

0, 0, 0, 3, 15, 45, 147, 402, 1134, 2991, 7917, 20367, 52167, 131748, 330876, 824187, 2042763, 5035473, 12361755, 30226614, 73664298, 178971879, 433649769, 1048133619, 2527706127, 6083434824, 14613750648, 35045236083, 83909261319

Offset: 0

Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 21 2002

nonn

Coefficient of q^0 is A006130.

			The first 6 nu polynomials are nu(0)=1, nu(1)=1, nu(2)=4, nu(3)=7+3q, nu(4)=19+15q+12q^2, nu(5)=40+45q+42q^2+30q^3+9q^4, so the coefficients of q^1 are 0,0,0,3,15,45.

M. Beattie, S. Dăscălescu and S. Raianu, Lifting of Nichols Algebras of Type B_2, arXiv:math/0204075 [math.QA], 2002.

Coefficient of q^0, q^2 and q^3 are in A006130, A074356 and A074357. Related sequences with other values of b and lambda are in A074082-A074089, A074352-A074354, A074358-A074363.

nu := proc(n,b,lambda) option remember ; if n = 0 then 1 ; elif n = 1 then b ; else b*nu(n-1,b,lambda)+lambda*nu(n-2,b,lambda)*add(q^i,i=0..n-2) ; fi ; end:
A074355 := proc(n) local b,lambda,thisnu ; b := 1 ; lambda := 3 ; thisnu := nu(n,b,lambda) ; RETURN( coeftayl(thisnu,q=0,1) ) ; end: # R. J. Mathar, Mar 20 2007

nu[n_, b_, lambda_] := nu[n, b, lambda] = Which[ n == 0, 1, n == 1, b, True, b*nu[n - 1, b, lambda] + lambda*nu[n - 2, b, lambda]*Sum[q^i, {i, 0, n - 2}]];
a[n_] := a[n] = Coefficient[nu[n, 1, 3], q, 1];
Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 30}] (* Jean-François Alcover, Nov 23 2017, from 1st Maple program *)

G.f.: (9x^4+3x^3)/(1-3x-3x^2)^2 (conjectured). - Ralf Stephan, May 09 2004

More terms from R. J. Mathar, Mar 20 2007

A074361 Coefficient of q^1 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=bnu(n-1)+lambda(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(3,1).

Original entry on oeis.org

0, 0, 0, 3, 19, 93, 407, 1674, 6618, 25455, 95953, 356151, 1305887, 4741092, 17072484, 61055787, 217074895, 767882865, 2704365719, 9487509102, 33170122494, 115614094071, 401864286637, 1393378817259, 4820368210175

Offset: 0

Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 21 2002

nonn

Coefficient of q^0 is A006190(n+1).

			The first 6 nu polynomials are nu(0)=1, nu(1)=3, nu(2)=10, nu(3)=33+3q, nu(4)=109+19q+10q^2, nu(5)=360+93q+66q^2+36q^3+3q^4, so the coefficients of q^1 are 0,0,0,3,19,93.

M. Beattie, S. Dăscălescu and S. Raianu, Lifting of Nichols Algebras of Type B_2, arXiv:math/0204075 [math.QA], 2002.
Index entries for linear recurrences with constant coefficients, signature (6, -7, -6, -1).

Coefficient of q^0, q^2 and q^3 are in A006190, A074362 and A074363. Related sequences with other values of b and lambda are in A074082-A074089, A074352-A074360.

CoefficientList[Series[(x^4+3x^3)/(1-3x-x^2)^2,{x,0,30}],x] (* or *) Join[{0},LinearRecurrence[{6,-7,-6,-1},{0,0,3,19},30]] (* Harvey P. Dale, Jan 16 2012 *)

G.f.: (x^4+3x^3)/(1-3x-x^2)^2.

a(0)=0, a(1)=0, a(2)=0, a(3)=3, a(4)=19, a(n)=6*a(n-1)-7*a(n-2)- 6*a(n-3)- a(n-4). - Harvey P. Dale, Jan 16 2012

More terms from Brent Lehman (mailbjl(AT)yahoo.com), Aug 25 2002

A074083 Coefficient of q^3 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=bnu(n-1)+lambda(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(1,1).

Original entry on oeis.org

0, 0, 0, 0, 0, 4, 14, 39, 97, 224, 494, 1051, 2177, 4412, 8784, 17228, 33360, 63886, 121164, 227833, 425147, 787916, 1451198, 2657821, 4842727, 8782230, 15857426, 28517864, 51095760, 91232520, 162372682, 288115147, 509790277, 899630376

Offset: 0

Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 19 2002

nonn

The coefficient of q^0 in nu(n) is the Fibonacci number F(n+1). The coefficient of q^1 is A023610(n-3).

			The first 6 nu polynomials are nu(0)=1, nu(1)=1, nu(2)=2, nu(3)=3+q, nu(4)=5+3q+2q^2, nu(5)=8+7q+6q^2+4q^3+q^4, so the coefficients of q^3 are 0,0,0,0,0,4.

M. Beattie, S. Dăscălescu and S. Raianu, Lifting of Nichols Algebras of Type B_2, arXiv:math/0204075 [math.QA], 2002.
Index entries for linear recurrences with constant coefficients, signature (4, -2, -8, 5, 8, -2, -4, -1).

Coefficients of q^0, q^1 and q^2 are in A000045, A023610 and A074082. Related sequences with different values of b and lambda are in A074084-A074089.

b=1; lambda=1; expon=3; nu[0]=1; nu[1]=b; nu[n_] := nu[n]=Together[b*nu[n-1]+lambda(1-q^(n-1))/(1-q)nu[n-2]]; a[n_] := Coefficient[nu[n], q, expon]
(* Second program: *)
Join[{0, 0, 0}, LinearRecurrence[{4, -2, -8, 5, 8, -2, -4, -1}, {0, 0, 4, 14, 39, 97, 224, 494}, 31]] (* Jean-François Alcover, Jan 27 2019 *)

G.f.: (4x^5-2x^6-9x^7+x^8+6x^9+2x^10)/(1-x-x^2)^4.

a(n) = 4a(n-1)-2a(n-2)-8a(n-3)+5a(n-4)+8a(n-5)-2a(n-6)-4a(n-7)-a(n-8) for n>=11.

Edited by Dean Hickerson, Aug 21 2002

A074088 Coefficient of q^2 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=bnu(n-1)+lambda(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(2,3).

Original entry on oeis.org

0, 0, 0, 0, 21, 120, 585, 2508, 10122, 39042, 145974, 532704, 1907451, 6725004, 23407287, 80591148, 274899288, 930128646, 3124838844, 10432356000, 34634029713, 114403303008, 376184538165, 1231890463020, 4018920819606

Offset: 0

Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 19 2002

The coefficient of q^0 is A014983(n+1).

			The first 6 nu polynomials are nu(0)=1, nu(1)=2, nu(2)=7, nu(3)=20+6q, nu(4)=61+33q+21q^2, nu(5)=182+144q+120q^2+78q^3+18q^4, so the coefficients of q^2 are 0,0,0,0,21,120.

G. C. Greubel, Table of n, a(n) for n = 0..1000
M. Beattie, S. Dăscălescu and S. Raianu, Lifting of Nichols Algebras of Type B_2, arXiv:math/0204075 [math.QA], 2002.
Index entries for linear recurrences with constant coefficients, signature (6,-3,-28,9,54,27).

Coefficients of q^0, q^1 and q^3 are in A014983, A074087 and A074089. Related sequences with other values of b and lambda are in A074082-A074086.

I:=[0,0,21,120,585,2508]; [0,0] cat [n le 6 select I[n] else 6*Self(n-1) -3*Self(n-2) -28*Self(n-3) +9*Self(n-4) +54*Self(n-5) +27*Self(n-6): n in [1..30]]; // G. C. Greubel, May 26 2018

b=2; lambda=3; expon=2; nu[0]=1; nu[1]=b; nu[n_] := nu[n]=Together[b*nu[n-1]+lambda(1-q^(n-1))/(1-q)nu[n-2]]; a[n_] := Coefficient[nu[n], q, expon]
(* Second program: *)
Join[{0,0},LinearRecurrence[{6,-3,-28,9,54,27},{0,0,21,120,585,2508},40]] (* Harvey P. Dale, Apr 28 2012 *)

x='x+O('x^30); concat([0,0,0,0], Vec((21*x^4 -6*x^5 -72*x^6 -54*x^7)/(1-2*x-3*x^2)^3)) \\ G. C. Greubel, May 26 2018

G.f.: (21*x^4 -6*x^5 -72*x^6 -54*x^7)/(1-2*x-3*x^2)^3.

a(n) = 6*a(n-1) -3*a(n-2) -28*a(n-3) +9*a(n-4) +54*a(n-5) +27*a(n-6) for n>=8.

Edited by Dean Hickerson, Aug 21 2002

A074353 Coefficient of q^2 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=bnu(n-1)+lambda(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(1,2).

Original entry on oeis.org

0, 0, 0, 0, 6, 20, 70, 196, 542, 1396, 3526, 8628, 20766, 49092, 114598, 264356, 603998, 1368148, 3076166, 6870740, 15256158, 33696804, 74073510, 162127940, 353460766, 767816500, 1662394310, 3588252916, 7723318942, 16580031876, 35506388646, 75864499428

Offset: 0

Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 21 2002

Coefficient of q^0 is A001045(n+1).

			The first 6 nu polynomials are nu(0)=1, nu(1)=1, nu(2)=3, nu(3)=5+2q, nu(4)=11+8q+6q^2, nu(5)=21+22q+20q^2+14q^3+4q^4, so the coefficients of q^2 are 0,0,0,0,6,20.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
M. Beattie, S. Dăscălescu and S. Raianu, Lifting of Nichols Algebras of Type B_2, arXiv:math/0204075 [math.QA], 2002.
Index entries for linear recurrences with constant coefficients, signature (3,3,-11,-6,12,8).

Coefficients of q^0, q^1 and q^3 are in A001045, A074352 and A074354. Related sequences with other values of b and lambda are in A074082-A074089, A074355-A074363.

LinearRecurrence[{3, 3, -11, -6, 12, 8}, {0, 0, 0, 0, 6, 20, 70, 196}, 50] (* Paolo Xausa, Jan 28 2025 *)

concat(vector(4), Vec(2*x^4*(3 + x - 4*x^2 - 4*x^3) / ((1 + x)^3*(1 - 2*x)^3) + O(x^40))) \\ Colin Barker, Nov 18 2017

a(0)=0 for n>0, a(n) = (1/81)*(2^(n-1)*(6*n^2-43) + (-1)^n*(6*n^2-24*n+62)). - Benoit Cloitre, Jan 16 2003
From Colin Barker, Nov 18 2017: (Start)
G.f.: 2*x^4*(3 + x - 4*x^2 - 4*x^3) / ((1 + x)^3*(1 - 2*x)^3).
a(n) = 3*a(n-1) + 3*a(n-2) - 11*a(n-3) - 6*a(n-4) + 12*a(n-5) + 8*a(n-6) for n>7.
(End)

More terms from Benoit Cloitre, Jan 16 2003

Corrected by T. D. Noe, Oct 25 2006

A074356 Coefficient of q^2 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=bnu(n-1)+lambda(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(1,3).

Original entry on oeis.org

0, 0, 0, 0, 12, 42, 180, 561, 1833, 5373, 15798, 44367, 123561, 336243, 906054, 2408094, 6344832, 16561824, 42922602, 110472933, 282678423, 719404803, 1822117962, 4594816221, 11540742615, 28880919975, 72033463644, 179107709004

Offset: 0

Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 21 2002

nonn

Coefficient of q^0 is A006130.

			The first 6 nu polynomials are nu(0)=1, nu(1)=1, nu(2)=4, nu(3)=7+3q, nu(4)=19+15q+12q^2, nu(5)=40+45q+42q^2+30q^3+9q^4, so the coefficients of q^2 are 0,0,0,0,12,42.

M. Beattie, S. Dăscălescu and S. Raianu, Lifting of Nichols Algebras of Type B_2, arXiv:math/0204075 [math.QA], 2002.

Coefficient of q^0, q^1 and q^3 are in A006130, A074355 and A074357. Related sequences with other values of b and lambda are in A074082-A074089, A074352-A074354, A074358-A074363.

nu := proc(n,b,lambda) if n = 0 then 1 ; elif n = 1 then b ; else b*nu(n-1,b,lambda)+lambda*nu(n-2,b,lambda)*add(q^i,i=0..n-2) ; fi ; end: A074356 := proc(n) local b,lambda,thisnu ; b := 1 ; lambda := 3 ; thisnu := nu(n,b,lambda) ; RETURN( coeftayl(thisnu,q=0,2) ) ; end: for n from 0 to 40 do printf("%d, ",A074356(n) ) ; od ; # R. J. Mathar, Mar 20 2007

nu[n_, b_, lambda_] := nu[n, b, lambda] = Which[n == 0, 1, n == 1, b, True, b*nu[n - 1, b, lambda] + lambda*nu[n - 2, b, lambda]*Sum[q^i, {i, 0, n - 2}]];
a[n_] := a[n] = Coefficient[nu[n, 1, 3], q, 2];
Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 30}] (* Jean-François Alcover, Nov 23 2017, from Maple *)

Conjectures from Colin Barker, Nov 18 2017: (Start)
G.f.: 3*x^4*(2 - 3*x)*(2 + 4*x + 3*x^2) / (1 - x - 3*x^2)^3.
a(n) = 3*a(n-1) + 6*a(n-2) - 17*a(n-3) - 18*a(n-4) + 27*a(n-5) + 27*a(n-6) for n>7.
(End)

More terms from R. J. Mathar, Mar 20 2007

A074359 Coefficient of q^2 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=bnu(n-1)+lambda(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(2,2).

Original entry on oeis.org

0, 0, 0, 0, 12, 64, 280, 1088, 3968, 13856, 46912, 155136, 503616, 1610496, 5086336, 15895552, 49229312, 151275008, 461662208, 1400356864, 4224703488, 12683452416, 37911164928, 112865394688, 334788444160, 989756825600

Offset: 0

Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 21 2002

nonn

Coefficient of q^0 is A002605.

			The first 6 nu polynomials are nu(0)=1, nu(1)=2, nu(2)=6, nu(3)=16+4q, nu(4)=44+20q+12q^2, nu(5)=120+80q+64q^2+40q^3+8q^4, so the coefficients of q^2 are 0,0,0,0,12,64.

M. Beattie, S. Dăscălescu and S. Raianu, Lifting of Nichols Algebras of Type B_2, arXiv:math/0204075 [math.QA], 2002.
Index entries for linear recurrences with constant coefficients, signature (6, -6, -16, 12, 24, 8).

Coefficient of q^0, q^1 and q^3 are in A002605, A074358 and A074360. Related sequences with other values of b and lambda are in A074082-A074089, A074352-A074357, A074361-A074363.

nu := proc(n,b,lambda) if n = 0 then 1 ; elif n = 1 then b ; else b*nu(n-1,b,lambda)+lambda*nu(n-2,b,lambda)*add(q^i,i=0..n-2) ; fi ; end: A074359 := proc(n) local b,lambda,thisnu ; b := 2 ; lambda := 2 ; thisnu := nu(n,b,lambda) ; RETURN( coeftayl(thisnu,q=0,2) ) ; end: for n from 0 to 40 do printf("%d, ",A074359(n) ) ; od ; # R. J. Mathar, Mar 20 2007

Join[{0, 0}, LinearRecurrence[{6, -6, -16, 12, 24, 8}, {0, 0, 12, 64, 280, 1088}, 24]] (* Jean-François Alcover, Sep 23 2017 *)

Conjecture: O.g.f: 4*x^4*(-3+2*x+8*x^2+4*x^3)/(2*x^2+2*x-1)^3. - R. J. Mathar, Jul 22 2009

More terms from R. J. Mathar, Mar 20 2007

A074085 Coefficient of q^2 in nu(n), where nu(0) = 1, nu(1) = b and, for n >= 2, nu(n) = bnu(n-1) + lambda(1 + q + q^2 + ... + q^(n - 2))*nu(n-2) with (b,lambda) = (2,1).

Original entry on oeis.org

0, 0, 0, 0, 5, 24, 91, 308, 978, 2978, 8802, 25440, 72251, 202316, 559941, 1534548, 4170256, 11250630, 30158900, 80389600, 213204513, 562896832, 1480086111, 3877337556, 10123000126, 26347306474, 68378847990, 176994780672

Offset: 0

Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 19 2002

nonn

The coefficient of q^0 is the Pell number A000129(n+1).

			The first 6 nu polynomials are nu(0) = 1, nu(1) = 2, nu(2) = 5, nu(3) = 12 + 2*q, nu(4) = 29 + 9*q + 5*q^2, nu(5) = 70 + 32q + 24*q^2 + 14*q^3 + 2*q^4, so the coefficients of q^2 are 0,0,0,0,5,24.

M. Beattie, S. Dăscălescu and S. Raianu, Lifting of Nichols Algebras of Type B_2, arXiv:math/0204075 [math.QA], 2002.
Index entries for linear recurrences with constant coefficients, signature (6, -9, -4, 9, 6, 1).

Coefficients of q^0, q^1 and q^3 are in A000129, A074084 and A074086. Related sequences with other values of b and lambda are in A074082-A074083 and A074087-A074089.

b=2; lambda=1; expon=2; nu[0]=1; nu[1]=b; nu[n_] := nu[n]=Together[b*nu[n-1]+lambda(1-q^(n-1))/(1-q)nu[n-2]]; a[n_] := Coefficient[nu[n], q, expon]
(* Second program: *)
Join[{0,0}, LinearRecurrence[{6, -9, -4, 9, 6, 1}, {0, 0, 5, 24, 91, 308}, 30]] (* Jean-François Alcover, Dec 13 2018 *)

G.f.: (5*x^4 - 6*x^5 - 8*x^6 - 2*x^7)/(1 - 2*x - x^2)^3.

a(n) = 6*a(n-1) - 9*a(n-2) - 4*a(n-3) + 9*a(n-4) + 6*a(n-5) + a(n-6) for n >= 8.

Edited by Dean Hickerson, Aug 21 2002

A074362 Coefficient of q^2 in nu(n), where nu(0) = 1, nu(1) = b and, for n >= 2, nu(n) = bnu(n-1) + lambda(1 + q + q^2 + ... + q^(n-2))*nu(n-2) with (b,lambda) = (3,1).

Original entry on oeis.org

0, 0, 0, 0, 10, 66, 336, 1527, 6513, 26667, 106102, 413265, 1583331, 5986689, 22392606, 83002842, 305308666, 1115587020, 4052786850, 14648359515, 52705460583, 188868467853, 674332868566, 2399653030899, 8513523719661

Offset: 0

Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 21 2002

nonn

Coefficient of q^0 is A006190(n+1).

			The first 6 nu polynomials are nu(0) = 1, nu(1) = 3, nu(2) = 10, nu(3) = 33 + 3*q, nu(4) = 109 + 19*q + 10*q^2, nu(5) = 360 + 93*q + 66*q^2 + 36*q^3 + 3*q^4, so the coefficients of q^1 are 0,0,0,0,10,66.

M. Beattie, S. Dăscălescu and S. Raianu, Lifting of Nichols Algebras of Type B_2, arXiv:math/0204075 [math.QA], 2002.
Index entries for linear recurrences with constant coefficients, signature (9, -24, 9, 24, 9, 1).

Coefficient of q^0, q^1 and q^3 are in A006190, A074361 and A074363. Related sequences with other values of b and lambda are in A074082-A074089, A074352-A074360.

Join[{0, 0}, LinearRecurrence[{9, -24, 9, 24, 9, 1}, {0, 0, 10, 66, 336, 1527}, 30]] (* Jean-François Alcover, Dec 13 2018 *)

G.f.: (-3*x^7 - 18*x^6 - 24*x^5 + 10*x^4)/(1 - 3*x - x^2)^3.

More terms from Brent Lehman (mailbjl(AT)yahoo.com), Aug 25 2002

cp's OEIS Frontend

A074355 Coefficient of q^1 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=b*nu(n-1)+lambda*(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(1,3).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

Extensions

A074361 Coefficient of q^1 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=b*nu(n-1)+lambda*(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(3,1).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A074083 Coefficient of q^3 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=b*nu(n-1)+lambda*(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(1,1).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A074088 Coefficient of q^2 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=b*nu(n-1)+lambda*(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(2,3).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

Extensions

A074353 Coefficient of q^2 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=b*nu(n-1)+lambda*(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(1,2).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A074356 Coefficient of q^2 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=b*nu(n-1)+lambda*(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(1,3).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

Extensions

A074359 Coefficient of q^2 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=b*nu(n-1)+lambda*(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(2,2).

Views

A074355 Coefficient of q^1 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=bnu(n-1)+lambda(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(1,3).

A074361 Coefficient of q^1 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=bnu(n-1)+lambda(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(3,1).

A074083 Coefficient of q^3 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=bnu(n-1)+lambda(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(1,1).

A074088 Coefficient of q^2 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=bnu(n-1)+lambda(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(2,3).

A074353 Coefficient of q^2 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=bnu(n-1)+lambda(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(1,2).

A074356 Coefficient of q^2 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=bnu(n-1)+lambda(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(1,3).

A074359 Coefficient of q^2 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=bnu(n-1)+lambda(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(2,2).

A074085 Coefficient of q^2 in nu(n), where nu(0) = 1, nu(1) = b and, for n >= 2, nu(n) = bnu(n-1) + lambda(1 + q + q^2 + ... + q^(n - 2))*nu(n-2) with (b,lambda) = (2,1).

A074362 Coefficient of q^2 in nu(n), where nu(0) = 1, nu(1) = b and, for n >= 2, nu(n) = bnu(n-1) + lambda(1 + q + q^2 + ... + q^(n-2))*nu(n-2) with (b,lambda) = (3,1).