|
| |
|
|
A154153
|
|
Indices n such that 28 plus the n-th triangular number is a perfect square.
|
|
2
| |
|
|
6, 8, 47, 57, 278, 336, 1623, 1961, 9462, 11432, 55151, 66633, 321446, 388368, 1873527, 2263577, 10919718, 13193096, 63644783, 76895001
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
LINKS
| F. T. Adams-Watters, SeqFan Discussion, Oct 2009
|
|
|
FORMULA
| {k: 28+k*(k+1)/2 in A000290}
Conjecture: a(n)= +a(n-1) +6*a(n-2) -6*a(n-3) -a(n-4) +a(n-5)
Conjecture: G.f.: x*(-6-2*x-3*x^2+2*x^3+7*x^4)/((x-1) * (x^2-2*x-1) * (x^2+2*x-1)) = (14+1/(x-1)+(14+29*x)/(x^2-2*x-1)+(-1-12*x)/(x^2+2*x-1))/2 .
|
|
|
EXAMPLE
| 6*(6+1)/2+28 = 7^2. 8*(8+1)/2+28 = 8^2. 47*(47+1)/2+28 = 34^2. 57*(57+1)/2+28 = 41^2.
|
|
|
PROG
| (PARI) {for (n=0, 10^9, if ( issquare(n*(n+1)\2 + 28), print1(n, ", ") ) ); }
|
|
|
CROSSREFS
| Cf. A000217, A000290, A006451.
Sequence in context: A038262 A054102 A000380 * A164640 A192158 A167481
Adjacent sequences: A154150 A154151 A154152 * A154154 A154155 A154156
|
|
|
KEYWORD
| nonn,more
|
|
|
AUTHOR
| R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 18 2009
|
| |
|
|
