A062123 a(n) = (9n^2 + 9n + 4)/2.

2, 11, 29, 56, 92, 137, 191, 254, 326, 407, 497, 596, 704, 821, 947, 1082, 1226, 1379, 1541, 1712, 1892, 2081, 2279, 2486, 2702, 2927, 3161, 3404, 3656, 3917, 4187, 4466, 4754, 5051, 5357, 5672, 5996, 6329, 6671, 7022, 7382, 7751, 8129, 8516, 8912, 9317

Offset: 0

Author

Vladeta Jovovic, Jun 04 2001

Keywords

• nonn
• easy

Comments

Third column of A046741.

References

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

Links

• Harry J. Smith, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. dumbbells: A002940, A002941, A002889, A046741, A055608, A062124-A062127.

Cf. A235332.

Programs

GAP

List([0..50], n -> 2 +9*n*(1+n)/2); # G. C. Greubel, Jan 31 2019

Magma

[2 +9*n*(1+n)/2: n in [0..50]]; // G. C. Greubel, Jan 31 2019

Mathematica

Table[2 +9*n*(1+n)/2, {n,0,50}] (* G. C. Greubel, Jan 31 2019 *)
LinearRecurrence[{3,-3,1},{2,11,29},50] (* Harvey P. Dale, Jan 12 2020 *)

PARI

for (n=0, 1000, write("b062123.txt", n, " ", 2 + (n + n^2)*9/2) ) \\ Harry J. Smith, Aug 02 2009

Sage

[2 +9*n*(1+n)/2 for n in range(50)] # G. C. Greubel, Jan 31 2019

Formula

G.f.: (1+2*x)*(2+x)/(1-x)^3. 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) = 9*n + a(n-1), with n>0, a(0)=2. - Vincenzo Librandi, Aug 07 2010

E.g.f.: (4 +18*x +9*x^2)*exp(x)/2. - G. C. Greubel, Jan 31 2019

Extensions

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