A062123 -id:A062123 - cp's OEIS frontend

A002940 Arrays of dumbbells.

1, 4, 11, 26, 56, 114, 223, 424, 789, 1444, 2608, 4660, 8253, 14508, 25343, 44030, 76136, 131110, 224955, 384720, 656041, 1115784, 1893216, 3205416, 5416441, 9136084, 15384563, 25866914, 43429784, 72821274, 121953943, 204002680, 340886973, 569047468, 949022608

Offset: 1

N. J. A. Sloane

Whitney transform of n. The Whitney transform maps the sequence with g.f. g(x) to that with g.f. (1/(1-x))g(x(1+x)). - Paul Barry, Feb 16 2005
a(n-1) is the permanent of the n X n 0-1 matrix with 1 in (i,j) position iff (i=1 and j1). For example, with n=5, a(4) = per([[1, 1, 1, 1, 0], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [0, 1, 1, 1, 1], [0, 0, 1, 1, 1]]) = 26. - David Callan, Jun 07 2006
a(n) is the internal path length of the Fibonacci tree of order n+2. A Fibonacci tree of order n (n>=2) is a complete binary tree whose left subtree is the Fibonacci tree of order n-1 and whose right subtree is the Fibonacci tree of order n-2; each of the Fibonacci trees of order 0 and 1 is defined as a single node. The internal path length of a tree is the sum of the levels of all of its internal (i.e. non-leaf) nodes. - Emeric Deutsch, Jun 15 2010
Partial Sums of A023610 - John Molokach, Jul 03 2013

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983,(2.3.14).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. E. Knuth, The Art of Computer Programming, Vol. 3, 2nd edition, Addison-Wesley, Reading, MA, 1998, p. 417.

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Carlos Alirio Rico Acevedo and Ana Paula Chaves, Double-Recurrence Fibonacci Numbers and Generalizations, arXiv:1903.07490 [math.NT], 2019.
Ricardo Gómez Aíza, Trees with flowers: A catalog of integer partition and integer composition trees with their asymptotic analysis, arXiv:2402.16111 [math.CO], 2024. See pp. 23-24.
R. C. Grimson, Exact formulas for 2 x n arrays of dumbbells, J. Math. Phys., 15 (1974), 214-216.
R. C. Grimson, Exact formulas for 2 x n arrays of dumbbells, J. Math. Phys., 15.2 (1974), 214-216. (Annotated scanned copy)
Y. Horibe, An entropy view of Fibonacci trees, Fibonacci Quarterly, 20, No. 2, 1982, 168-178.
R. B. McQuistan and S. J. Lichtman, Exact recursion relation for 2 x N arrays of dumbbells, J. Math. Phys., 11 (1970), 3095-3099.
Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,1,1).

Cf. A002941, A002889, A055608, A062123, A062124, A062125, A062126, A062127, A046741.

Cf. A000045, A001925, A023610, A054454, A006478, A067331, A178523.

a002940 n = a002940_list !! (n-1)
a002940_list = 1 : 4 : 11 : zipWith (+)
   (zipWith (-) (map (* 2) $ drop 2 a002940_list) a002940_list)
   (drop 5 a000045_list)
-- Reinhard Zumkeller, Jan 18 2014

m:=35; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( (1+x)/((1-x)*(1-x-x^2)^2) )); // G. C. Greubel, Jan 31 2019

a[n_]:= a[n]= If[n<3, n^2, 2a[n-1] -a[n-3] +Fibonacci[n+1]]; Array[a, 32] (* Jean-François Alcover, Jul 31 2018 *)

my(x='x+O('x^35)); Vec((1+x)/((1-x)*(1-x-x^2)^2)) \\ G. C. Greubel, Jan 31 2019

((1+x)/((1-x)*(1-x-x^2)^2)).series(x, 35).coefficients(x, sparse=False) # G. C. Greubel, Jan 31 2019

a(n) = 2*a(n-1) - a(n-3) + A000045(n+1).
G.f.: x*(1+x)/((1-x)*(1-x-x^2)^2).
a(n) = Sum_{k=0..n} ( Sum_{i=0..n} k*C(k, i-k) ). - Paul Barry, Feb 16 2005
E.g.f.: 2*exp(x) + exp(x/2)*((55*x - 50)*cosh(sqrt(5)*x/2) + sqrt(5)*(25*x - 22)*sinh(sqrt(5)*x/2))/25. - Stefano Spezia, Dec 03 2023

More terms from Henry Bottomley, Jun 02 2000

A002941 Arrays of dumbbells.

Original entry on oeis.org

1, 7, 29, 94, 263, 667, 1577, 3538, 7622, 15900, 32314, 64274, 125561, 241569, 458715, 861242, 1601081, 2950693, 5396209, 9801012, 17692092, 31759800, 56727588, 100861716, 178585489, 314995915, 553650761, 969967510, 1694235803

Offset: 1

N. J. A. Sloane

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983,(2.3.14).
R. C. Grimson, Exact formulas for 2 x n arrays of dumbbells, J. Math. Phys., 15 (1974), 214-216.
R. B. McQuistan and S. J. Lichtman, Exact recursion relation for 2 x N arrays of dumbbells, J. Math. Phys., 11 (1970), 3095-3099.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
R. C. Grimson, Exact formulas for 2 x n arrays of dumbbells, J. Math. Phys., 15.2 (1974), 214-216. (Annotated scanned copy)
Index entries for linear recurrences with constant coefficients, signature (5,-7,-2,10,-2,-5,1,1).

Cf. A046741, A002940, A002889, A055608, A062123-A062127.

a002941 n = a002941_list !! (n-1)
a002941_list = 1 : 7 : 29 : zipWith (+)
   (zipWith (-) (map (* 2) $ drop 2 a002941_list) a002941_list)
   (drop 2 $ zipWith (+) (tail a002940_list) a002940_list)
-- Reinhard Zumkeller, Jan 18 2014

m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( (1+x)^2/((1-x-x^2)^3*(1-x)^2) )); // G. C. Greubel, Jan 31 2019

CoefficientList[(1+x)^2/((1-x-x^2)^3*(1-x)^2) + O[x]^30, x] (* Jean-François Alcover, Jul 31 2018 *)
LinearRecurrence[{5,-7,-2,10,-2,-5,1,1},{1,7,29,94,263,667,1577,3538},30] (* Harvey P. Dale, Aug 29 2021 *)

x='x+O('x^30); Vec((1+x)^2/((1-x-x^2)^3*(1-x)^2)) \\ Altug Alkan, Jul 31 2018

((1+x)^2/((1-x-x^2)^3*(1-x)^2)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 31 2019

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

a(n) = 2*a(n-1) - a(n-3) + A002940(n) + A002940(n-1).

More terms from Henry Bottomley, Jun 02 2000

A002889 Arrays of dumbbells.

Original entry on oeis.org

1, 10, 56, 234, 815, 2504, 7018, 18336, 45328, 107160, 244198, 539656, 1161987, 2446906, 5054440, 10266850, 20549117, 40595568, 79271188, 153190480, 293278496, 556737696, 1048772300, 1961855408, 3646420325, 6737649754

Offset: 1

N. J. A. Sloane

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983,(2.3.14).
R. C. Grimson, Exact formulas for 2 x n arrays of dumbbells, J. Math. Phys., 15 (1974), 214-216.
R. B. McQuistan and S. J. Lichtman, Exact recursion relation for 2 x N arrays of dumbbells, J. Math. Phys., 11 (1970), 3095-3099.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
R. C. Grimson, Exact formulas for 2 x n arrays of dumbbells, J. Math. Phys., 15.2 (1974), 214-216. (Annotated scanned copy)
Index entries for linear recurrences with constant coefficients, signature (7,-17,11,19,-29,-3,21,-3,-7,1,1).

Cf. A046741, A002940, A002941.

Cf. A055608, A062123-A062127.

a002889 n = a002889_list !! (n-1)
a002889_list = 1 : 10 : 56 : zipWith (+)
   (zipWith (-) (map (* 2) $ drop 2 a002889_list) a002889_list)
   (drop 2 $ zipWith (+) (tail a002941_list) a002941_list)
-- Reinhard Zumkeller, Jan 18 2014

m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( (1+x)^3/((1-x)^3*(1-x-x^2)^4) )); // G. C. Greubel, Jan 31 2019

CoefficientList[(1+x)^3/((1-x)^3*(1-x-x^2)^4) + O[x]^30, x] (* Jean-François Alcover, Jul 31 2018 *)
LinearRecurrence[{7,-17,11,19,-29,-3,21,-3,-7,1,1},{1,10,56,234,815,2504,7018,18336,45328,107160,244198},30] (* Harvey P. Dale, Jul 25 2021 *)

x='x+O('x^30); Vec((1+x)^3/((1-x)^3*(1-x-x^2)^4)) \\ Altug Alkan, Jul 31 2018

((1+x)^3/((1-x)^3*(1-x-x^2)^4)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 31 2019

a(n) = 2*a(n-1) - a(n-3) + A002941(n) + A002941(n-1).

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

More terms from Henry Bottomley, Jun 02 2000

A055608 Arrays of dumbbells.

Original entry on oeis.org

1, 13, 92, 473, 1982, 7191, 23431, 70234, 196941, 522939, 1327002, 3240917, 7660538, 17602967, 39466363, 86593478, 186399956, 394478234, 822229746, 1690521204, 3433033150, 6893852746, 13702694284, 26982983126, 52680389239

Offset: 1

Henry Bottomley, Jun 02 2000

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983,(2.3.14).
R. C. Grimson, Exact formulas for 2 x n arrays of dumbbells, J. Math. Phys., 15 (1974), 214-216.
R. B. McQuistan and S. J. Lichtman, Exact recursion relation for 2 x N arrays of dumbbells, J. Math. Phys., 11 (1970), 3095-3099.

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (9,-31,44,4,-84,66,46,-74,-4,36,-4,-9,1,1).

Cf. A002940, A002941, A002889, A046741.

Cf. A062123-A062127.

a055608 n = a055608_list !! (n-1)
a055608_list = 1 : 13 : 92 : zipWith (+)
   (zipWith (-) (map (* 2) $ drop 2 a055608_list) a055608_list)
   (drop 2 $ zipWith (+) (tail a002889_list) a002889_list)
-- Reinhard Zumkeller, Jan 18 2014

m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( (1+x)^4/((1-x)^4*(1-x-x^2)^5) )); // G. C. Greubel, Jan 31 2019

CoefficientList[Series[(1+x)^4/((1-x)^4*(1-x-x^2)^5), {x,0,30}], x] (* G. C. Greubel, Jan 31 2019 *)

my(x='x+O('x^30)); Vec((1+x)^4/((1-x)^4*(1-x-x^2)^5)) \\ G. C. Greubel, Jan 31 2019

((1+x)^4/((1-x)^4*(1-x-x^2)^5)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 31 2019

G.f.: (1+x)^4/((1-x)^4*(1-x-x^2)^5).

a(n) = 2*a(n-1) - a(n-3) + A002889(n) + A002889(n-1).

A062127 Seventh column of A046741.

Original entry on oeis.org

13, 223, 1577, 7018, 23431, 64316, 153190, 327718, 644573, 1185025, 2061259, 3423422, 5467399, 8443318, 12664784, 18518842, 26476669, 37104995, 51078253, 69191458, 92373815, 121703056, 158420506, 203946878, 259898797, 328106053

Offset: 0

Vladeta Jovovic, Jun 04 2001

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983, (2.3.14).

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Cf. dumbbells: A002940, A002941, A002889, A046741, A055608, A062123-A062127.

List([0..40], n -> (81*n^6 +567*n^5 +2205*n^4 +4545*n^3 +5674*n^2 +3728*n +1040)/80); # G. C. Greubel, Jan 31 2019

[(81*n^6 +567*n^5 +2205*n^4 +4545*n^3 +5674*n^2 +3728*n +1040)/80: n in [0..40]]; // G. C. Greubel, Jan 31 2019

Table[(81*n^6 +567*n^5 +2205*n^4 +4545*n^3 +5674*n^2 +3728*n +1040)/80, {n, 0, 40}] (* G. C. Greubel, Jan 31 2019 *)
LinearRecurrence[{7,-21,35,-35,21,-7,1},{13,223,1577,7018,23431,64316,153190},30] (* Harvey P. Dale, Jun 07 2022 *)

vector(40, n, n--; (81*n^6 +567*n^5 +2205*n^4 +4545*n^3 +5674*n^2 +3728*n +1040)/80) \\ G. C. Greubel, Jan 31 2019

[(81*n^6 +567*n^5 +2205*n^4 +4545*n^3 +5674*n^2 +3728*n +1040)/80 for n in range(40)] # G. C. Greubel, Jan 31 2019

G.f.: (2*x^6 + 14*x^5 + 72*x^4 + 207*x^3 + 289*x^2 + 132*x + 13)/(1-x)^7. Generally, g.f. for k-th column of A046741 is coefficient of y^k in expansion of (1-y)/((1-y-y^2)*(1-y)-(1+y)*x).
From G. C. Greubel, Jan 31 2019: (Start)
a(n) = (81*n^6 + 567*n^5 + 2205*n^4 + 4545*n^3 + 5674*n^2 + 3728*n + 1040)/80.
E.g.f.: (1040 + 16800*x + 45760*x^2 + 39240*x^3 + 13140*x^4 + 1782*x^5 + 81*x^6)*exp(x)/80. (End)

More terms from Larry Reeves (larryr(AT)acm.org), Jun 06 2001

A235332 a(n) = n(9n + 25)/2 + 6.

Original entry on oeis.org

6, 23, 49, 84, 128, 181, 243, 314, 394, 483, 581, 688, 804, 929, 1063, 1206, 1358, 1519, 1689, 1868, 2056, 2253, 2459, 2674, 2898, 3131, 3373, 3624, 3884, 4153, 4431, 4718, 5014, 5319, 5633, 5956, 6288, 6629, 6979, 7338, 7706, 8083, 8469, 8864, 9268, 9681, 10103

Offset: 0

Bruno Berselli, Jan 22 2014

This is the case d=6 of n*(9*n + 4*d + 1)/2 + d. Other similar sequences are:
d=0, A022267;
d=1, A064225;
d=2, A062123;
d=3, A064226;
d=4, A022266 (with initial 0);
d=5, A178977.
First bisection of A235537.

Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A017257 (first differences), A022266, A022267, A062123, A064225, A064226, A081267, A178977, A235537.

Magma
```
[n*(9*n+25)/2+6: n in [0..50]];
```

Table[n (9 n + 25)/2 + 6, {n, 0, 50}]
LinearRecurrence[{3,-3,1},{6,23,49},50] (* Harvey P. Dale, Feb 12 2022 *)

a(n)=n*(9*n+25)/2+6 \\ Charles R Greathouse IV, Oct 07 2015

G.f.: (6 + 5*x - 2*x^2)/(1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
2*a(n) - a(n+1) + 12 = A081267(n).
E.g.f.: exp(x)*(12 + 34*x + 9*x^2)/2. - Elmo R. Oliveira, Nov 13 2024

A062124 Fourth column of A046741.

Original entry on oeis.org

3, 26, 94, 234, 473, 838, 1356, 2054, 2959, 4098, 5498, 7186, 9189, 11534, 14248, 17358, 20891, 24874, 29334, 34298, 39793, 45846, 52484, 59734, 67623, 76178, 85426, 95394, 106109, 117598, 129888, 143006, 156979, 171834, 187598, 204298

Offset: 0

Vladeta Jovovic, Jun 04 2001

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983, (2.3.14).

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

Cf. dumbbells: A002940, A002941, A002889, A046741, A055608, A062123-A062127.

List([0..40], n -> (6+19*n+18*n^2+9*n^3)/2); # G. C. Greubel, Jan 31 2019

[(6+19*n+18*n^2+9*n^3)/2: n in [0..40]]; // G. C. Greubel, Jan 31 2019

Table[(6+19*n+18*n^2+9*n^3)/2, {n,0,40}] (* G. C. Greubel, Jan 31 2019 *)
LinearRecurrence[{4,-6,4,-1},{3,26,94,234},40] (* Harvey P. Dale, Feb 20 2022 *)

vector(40, n, n--; (6+19*n+18*n^2+9*n^3)/2) \\ G. C. Greubel, Jan 31 2019

[(6+19*n+18*n^2+9*n^3)/2 for n in range(40)] # G. C. Greubel, Jan 31 2019

G.f.: (3 + 14*x + 8*x^2 + 2*x^3)/(1-x)^4. Generally, g.f. for k-th column of A046741 is coefficient of y^k in expansion of (1-y)/((1-y-y^2)*(1-y) - (1+y)*x).
From G. C. Greubel, Jan 31 2019: (Start)
a(n) = (6 + 19*n + 18*n^2 + 9*n^3)/2.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
E.g.f.: (6 + 46*x + 45*x^2 + 9*x^3)*exp(x)/2. (End)

More terms from Larry Reeves (larryr(AT)acm.org), Jun 06 2001

A062125 Fifth column of A046741.

Original entry on oeis.org

5, 56, 263, 815, 1982, 4115, 7646, 13088, 21035, 32162, 47225, 67061, 92588, 124805, 164792, 213710, 272801, 343388, 426875, 524747, 638570, 769991, 920738, 1092620, 1287527, 1507430, 1754381, 2030513, 2338040, 2679257, 3056540

Offset: 0

Vladeta Jovovic, Jun 04 2001

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983, (2.3.14).

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Cf. dumbbells: A002940, A002941, A002889, A046741, A055608, A062123-A062127.

List([0..40], n -> (40+126*n+165*n^2+90*n^3+27*n^4)/8); # G. C. Greubel, Jan 31 2019

[(40+126*n+165*n^2+90*n^3+27*n^4)/8: n in [0..40]]; // G. C. Greubel, Jan 31 2019

LinearRecurrence[{5, -10, 10, -5, 1}, {5, 56, 263, 815, 1982}, 31] (* or *) CoefficientList[Series[(5+33x^2+10x^3+31x+2x^4)/(1-x)^5,{x,0,30}],x] (* Harvey P. Dale, Dec 21 2011 *)
Table[(40+126*n+165*n^2+90*n^3+27*n^4)/8, {n,0,40}] (* G. C. Greubel, Jan 31 2019 *)

vector(40, n, n--; (40+126*n+165*n^2+90*n^3+27*n^4)/8) \\ G. C. Greubel, Jan 31 2019

[(40+126*n+165*n^2+90*n^3+27*n^4)/8 for n in range(40)] # G. C. Greubel, Jan 31 2019

G.f.: (5 + 33*x^2 + 10*x^3 + 31*x + 2*x^4)/(1-x)^5. Generally, g.f. for k-th column of A046741 is coefficient of y^k in expansion of (1-y)/((1-y-y^2)*(1-y)-(1+y)*x).
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5), where a(0)=5, a(1)=56, a(2)=263, a(3)=815, a(4)=1982. - Harvey P. Dale, Dec 21 2011
From G. C. Greubel, Jan 31 2019: (Start)
a(n) = (40 + 126*n + 165*n^2 + 90*n^3 + 27*n^4)/8.
E.g.f.: (40 + 408*x + 624*x^2 + 252*x^3 + 27*x^4)*exp(x)/8. (End)

More terms from Larry Reeves (larryr(AT)acm.org), Jun 06 2001

A062126 Sixth column of A046741.

Original entry on oeis.org

8, 114, 667, 2504, 7191, 17266, 36482, 70050, 124882, 209834, 335949, 516700, 768233, 1109610, 1563052, 2154182, 2912268, 3870466, 5066063, 6540720, 8340715, 10517186, 13126374, 16229866, 19894838, 24194298, 29207329

Offset: 0

Vladeta Jovovic, Jun 04 2001

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983, (2.3.14).

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Cf. dumbbells: A002940, A002941, A002889, A046741, A055608, A062123-A062127.

List([0..40], n -> (320+1114*n+1515*n^2+1125*n^3+405*n^4+81*n^5 )/40); # G. C. Greubel, Jan 31 2019

[(320+1114*n+1515*n^2+1125*n^3+405*n^4+81*n^5)/40: n in [0..40]]; // G. C. Greubel, Jan 31 2019

Table[(320+1114*n+1515*n^2+1125*n^3+405*n^4+81*n^5)/40, {n, 0, 40}] (* G. C. Greubel, Jan 31 2019 *)

vector(40, n, n--; (320+1114*n+1515*n^2+1125*n^3+405*n^4 + 81*n^5)/40) \\ G. C. Greubel, Jan 31 2019

[(320+1114*n+1515*n^2+1125*n^3+405*n^4+81*n^5)/40 for n in range(40)] # G. C. Greubel, Jan 31 2019

G.f.: (x+2)*(2*x^4 + 8*x^3 + 36*x^2 + 31*x + 4)/(1-x)^6. Generally, g.f. for k-th column of A046741 is coefficient of y^k in expansion of (1-y)/((1 - y - y^2)*(1-y) - (1+y)*x).
From G. C. Greubel, Jan 31 2019: (Start)
a(n) = (320 + 1114*n + 1515*n^2 + 1125*n^3 + 405*n^4 + 81*n^5)/40.
E.g.f.: (320 + 4240*x + 8940*x^2 + 5580*x^3 + 1215*x^4 + 81*x^5)*exp(x)/40. (End)

More terms from Larry Reeves (larryr(AT)acm.org), Jun 06 2001

cp's OEIS Frontend

A002940 Arrays of dumbbells.

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A002941 Arrays of dumbbells.

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A002889 Arrays of dumbbells.

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A055608 Arrays of dumbbells.

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Haskell

Magma

Mathematica

PARI

Sage

Formula

A062127 Seventh column of A046741.

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GAP

Magma

Mathematica

PARI

Sage

Formula

Extensions

A235332 a(n) = n*(9*n + 25)/2 + 6.

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A235332 a(n) = n(9n + 25)/2 + 6.