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Number of base 30 n-digit numbers with adjacent digits differing by two or less.
+10
3
1, 30, 144, 700, 3418, 16736, 82098, 403274, 1982980, 9758780, 48058110, 236801010, 1167371680, 5757241450, 28403776808, 140176438936, 691982963722, 3416834220692, 16875210619810, 83360735329998, 411862694955416
COMMENTS
[Empirical] a(base,n)=a(base-1,n)+5^(n-1) for base>=2n-1; a(base,n)=a(base-1,n)+5^(n-1)-2 when base=2n-2
PROG
(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>2)+($[i+1]`-$[i]`>2))
CROSSREFS
Cf. Base 30 differing by one or less A126384.
Number of base 30 n-digit numbers with adjacent digits differing by three or less.
+10
2
1, 30, 198, 1330, 8990, 60998, 414910, 2827298, 19292018, 131778306, 900905082, 6163326750, 42189104748, 288930449010, 1979525532152, 13566774085658, 93007355721960, 637770486097522, 4374235089178342, 30006615117630438
COMMENTS
[Empirical] a(base,n)=a(base-1,n)+7^(n-1) for base>=3n-2; a(base,n)=a(base-1,n)+7^(n-1)-2 when base=3n-3
PROG
(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>3)+($[i+1]`-$[i]`>3))
Number of base 30 n-digit numbers with adjacent digits differing by four or less.
+10
1
1, 30, 250, 2130, 18290, 157782, 1365186, 11836674, 102784246, 893546734, 7774696328, 67691981738, 589674316476, 5138751184130, 44795493135264, 390582096696514, 3406186539096420, 29708773287301186, 259147729207407892
COMMENTS
[Empirical] a(base,n)=a(base-1,n)+9^(n-1) for base>=4n-3; a(base,n)=a(base-1,n)+9^(n-1)-2 when base=4n-4
PROG
(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>4)+($[i+1]`-$[i]`>4))
Number of base 30 n-digit numbers with adjacent digits differing by five or less.
+10
0
1, 30, 300, 3080, 31910, 332332, 3472294, 36356914, 381225854, 4001308564, 42025251756, 441585511330, 4641438979272, 48795642652634, 513063278382886, 5395138052943334, 56736497174383966, 596680299580096756
COMMENTS
[Empirical] a(base,n)=a(base-1,n)+11^(n-1) for base>=5n-4; a(base,n)=a(base-1,n)+11^(n-1)-2 when base=5n-5
PROG
(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>5)+($[i+1]`-$[i]`>5))
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