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A086601
Triangular numbers + 1 squared.
6
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
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
KEYWORD
nonn,easy
AUTHOR
Jon Perry, Jul 23 2003
STATUS
approved