A133324 7-gonal numbers which are sum of 2 consecutive 7-gonal numbers.

1, 144841, 927821665, 222590743768705, 1425873367156486249, 342076743178546829707489, 2191277630703059899650524953, 525702444955366082679116505052393, 3367548455158599463971494297793284977, 807897836210987628258457093971387133310617

Offset

1,2

Comments

We write (5*p^2-3*p)/2 = (5*r^2-3*r)/2 + (5*(r+1)^2-3*(r+1))/2 ; X=10*p-3 and Y=10*r+2 satisfy the Diophantine equation X^2=2*Y^2+41.

Both bisections of the sequence satisfy the recurrence relation b(n+2) = 1536796802*b(n+1)-b(n)-441829080.

Links

Colin Barker, Table of n, a(n) for n = 1..218

Index entries for linear recurrences with constant coefficients, signature (1,1536796802,-1536796802,-1,1).

Formula

a(n) = a(n-1)+1536796802*a(n-2)-1536796802*a(n-3)-a(n-4)+a(n-5). - Colin Barker, Dec 07 2014

G.f.: -x*(697*x^4+167145360*x^3-609119978*x^2+144840*x+1) / ((x-1)*(x^2-39202*x+1)*(x^2+39202*x+1)). - Colin Barker, Dec 05 2014

Example

a(2) = 2.5*241^2-1.5*241 = 144841 = 5*r^2+4*r+1 with r=170.

Maple

F:= gfun[rectoproc]({a(n) = a(n-1)+1536796802*a(n-2)-1536796802*a(n-3)-a(n-4)+a(n-5),
a(1)=1, a(2)=144841, a(3)=927821665, a(4)=222590743768705, a(5) = 1425873367156486249}, a(n), remember):
seq(F(n), n=1..20); # Robert Israel, Dec 07 2014

Mathematica

LinearRecurrence[{1, 1536796802, -1536796802, -1, 1}, {1, 144841, 927821665, 222590743768705, 1425873367156486249}, 20] (* Harvey P. Dale, Dec 21 2016 *)

Prog

(PARI) Vec(-x*(697*x^4+167145360*x^3-609119978*x^2+144840*x+1) / ((x-1)*(x^2-39202*x+1)*(x^2+39202*x+1)) + O(x^100)) \\ Colin Barker, Dec 05 2014

Crossrefs

Cf. A000566, A133327, A133328.

Sequence in context: A145742 A236995 A204641 * A348808 A209968 A233915

Adjacent sequences: A133321 A133322 A133323 * A133325 A133326 A133327

Keyword

nonn,easy

Author

Richard Choulet, Oct 18 2007

Extensions

More terms from Colin Barker, Dec 05 2014

Edited by Michel Marcus and Colin Barker, Dec 07 2014

Status

approved