A086601 Triangular numbers + 1 squared.

1, 4, 16, 49, 121, 256, 484, 841, 1369, 2116, 3136, 4489, 6241, 8464, 11236, 14641, 18769, 23716, 29584, 36481, 44521, 53824, 64516, 76729, 90601, 106276, 123904, 143641, 165649, 190096, 217156, 247009, 279841, 315844, 355216, 398161

Offset

0,2

Comments

Also number of n X 2 0..1 arrays with rows and columns unimodal (cf. A223620, column 2). - Georg Fischer, Nov 03 2021

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

R. J. Mathar, The number of binary nxm matrices with at most k 1's in each row or column, (2014) Table 2 column 2.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = (A000217(n) + 1)^2.

a(n) = (binomial(2+n,2) - binomial(n,1))^2. - Zerinvary Lajos, May 30 2006, corrected by R. J. Mathar, May 14 2014

a(n) = A000124(n)^2. - Omar E. Pol, Oct 30 2007

a(n) = 1 + A061316(n). Zerinvary Lajos, Apr 25 2008

G.f.: ( -1+x-6*x^2+x^3-x^4 ) / (x-1)^5. - R. J. Mathar, May 14 2014

Example

a(5) = (t(5)+1)^2 = 16^2 = 256.

Maple

A086601 := proc(n)
    (n+2+n^2)^2 /4 ;
end proc:
seq(A086601(n), n=0..20) ; # R. J. Mathar, May 14 2014

Mathematica

(Accumulate[Range[0, 40]]+1)^2 (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 4, 16, 49, 121}, 40] (* Harvey P. Dale, Jan 14 2020 *)

Prog

(PARI) w=vector(40, i, (t(i)+1)^2)

Crossrefs

Cf. A000124, A000217, A061316, A223620.

Sequence in context: A370019 A119005 A237986 * A224147 A227266 A114185

Adjacent sequences: A086598 A086599 A086600 * A086602 A086603 A086604

Keyword

nonn,easy

Author

Jon Perry, Jul 23 2003

Status

approved