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Also binomial transform of 6m+1 (A016921). Also diagonal of a square array.
Considering a one-parameter generalization of the princeps sequence:
a 2a 4a+1 8a+3 16a+6 32a+11
.. a 2a+1 4a+2 8a+3 16a+5
.... a+1 2a+1 4a+1 8a+2
we write it explicitly:
3a = 3a +1-1
6a = 6a +2-2
12a + 3=12a +4-1
24a + 9=24a +8+1
48a +18=48a+16+2
96a +33=96a+32+1
...............
Hence for a=0,1,2.. the infinite square array:
1 2 4 8 16 32
4 8 16 32 64 128
7 14 28 56 112 224
10 20 40 80 160 320
13 26 52 104 208 416
16 32 64 128 256 512
Antidiagonal sums: 1 6 19 48 109 234 487 996 A095264
Antidiag. differences: 1 2 3 4 5 6 7 8 A000027
Sums: 2 8 22 52 114 240 494 1004 2*A125128
Differences: 0 4 16 44 104 228 480 988 4*(0 before A125128 or A000295 with only one 0)
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