A262242 Triangular numbers representable as 2^x + 2^y.

3, 6, 10, 36, 66, 136, 528, 2080, 8256, 32896, 131328, 524800, 2098176, 8390656, 33558528, 134225920, 536887296, 2147516416, 8590000128, 34359869440, 137439215616, 549756338176, 2199024304128, 8796095119360, 35184376283136, 140737496743936, 562949970198528

Offset: 1

Author

Alex Ratushnyak, Sep 15 2015

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..502

Crossrefs

Cf. A000217, A225390, A226499, A227027, A259745, A259746.

Programs

Python

def isTriangular(a):
    sr = 1 << (int.bit_length(a) >> 1)
    a += a
    while a < sr*(sr+1):  sr>>=1
    b = sr>>1
    while b:
      s = sr+b
      if a >= s*(s+1):  sr = s
      b>>=1
    return (a==sr*(sr+1))
for a in range(1,200):
    for b in range(a):
        c = (1<
				

Formula

Conjectures from Colin Barker, Sep 16 2015: (Start)

a(n) = 2^(n-5)*(2^n+4) for n>5.

a(n) = 6*a(n-1)-8*a(n-2) for n>7.

G.f.: x*(240*x^6+28*x^5-70*x^4+24*x^3-2*x^2-12*x+3) / ((2*x-1)*(4*x-1)).

(End)